Answer:
d) g/2
Explanation:
We need to use one of Newton's equations of motion to find the position of the stone at any time t.
x(t) = x₀(t) + ut - ¹/₂at²
Where
x₀(t) = initial position of the stone.
x(t) - x₀(t) = distance traveled by the stone at any time.
u = initial velocity of the stone
a = acceleration of the stone
t = time taken
On both planets, before the stone was thrown by the astronaut, x = 0 and t = 0.
=> 0 = x₀(t)
=> x₀(t) = 0
On earth, when the stone returns into the hand of the astronaut at time T on earth, x = 0.
=> 0 = 0 + uT - ¹/₂gT² (a = g)
=> uT = ¹/₂gT²
=> g = 2u/T
On planet X, when the stone returns into the hand of the astronaut, time = 2T , x = 0.
=> 0 = 0 + u(2T) - ¹/₂a(2T)²
=> 2uT = 2aT²
=> a = u/T
By comparing we see that a = g/2.
Final answer:
The acceleration due to gravity on planet X is determined by comparing the time it takes for a stone thrown vertically upward to return to the thrower's hand. Using kinematic equations and given that it takes twice the time to return on planet X as it does on Earth, we deduce the acceleration on planet X is half that of Earth's gravity (g/2).
Explanation:
The question concerns finding the acceleration due to gravity on an unknown planet, which is an essential concept in physics. To determine the gravitational acceleration (g) on planet X, given that a stone thrown with the same initial upward velocity as on Earth returns in 2T instead of T, we can use the kinematic equations for motion under constant acceleration.
On Earth, the total time for the stone to return to the thrower's hand is T, which implies that the time to reach the maximum height is T/2. Applying the equation v = u + at, where v is the final velocity (0 m/s at maximum height), u is the initial upward velocity, a is the acceleration due to gravity (which is -g on Earth), and t is the time (T/2), we have 0 = u - g(T/2). Solving for u gives us u = g(T/2).
On Planet X, the total time for the stone to return to the thrower's hand is 2T, so the time to reach maximum height is T. Using the same equation with the acceleration on Planet X as aX, we get 0 = u - aX(T). Since u = g(T/2), we have g(T/2) = aX(T), leading to aX = g/2.
Therefore, the correct answer is (d) g/2.
A car went 60 km in 5/6 of an hour while a second car went 54 km in 2/3h. Which car was faster? How many times faster?
Answer:
The car that went 54 km in 2/3h was faster, 5/4 times faster than the other car
Explanation:
Average speed of a car is the ratio between the displacement [tex]\Delta x [/tex] and the time (t) it takes to do that displacement:
[tex]V_{avg}=\frac{\Delta x}{t} [/tex]
So, for the first car:
[tex]V_{avg1}=\frac{60km}{\frac{5h}{6}} =72\frac{km}{h} [/tex] (1)
for the second car we have:
[tex]V_{avg2}=\frac{60km}{\frac{2h}{3}} =90\frac{km}{h} [/tex] (2)
So, the second cart is faster than the first one. To find how many times divide speed 2 by speed 1:
[tex]\frac{90}{72}=\frac{5}{4} [/tex]
An overweight boy and a skinny girl are balanced on a massless seesaw. If they both move forward such that they are one-half their original distance from the pivot point, what will happen to the seesaw?
The seesaw will average out a little bit, and not be as tilted to one side as before.
A physics student with a stopwatch drops a rock into a very deep well, and measures the time between when he drops the rocks and when he hears the sound of the rock hitting the water below. If the speed of sound is 343 m/s, and the student measures a time of 6.20 s, how deep is the well?
Answer:
h= 161.06 m
Explanation:
Given that
Speed of the sound ,C= 343 m/s
Total time ,t= 6.2 s
lets take the depth of the well = h
The time taken by stone before striking the water = t₁
we know that
[tex]h=\dfrac{1}{2}gt_1^2[/tex]
[tex]t_1=\sqrt{\dfrac{2h}{g}}[/tex]
The time taken by sound =t₂
[tex]t_2=\dfrac{h}{343}[/tex]
The total time
t = t₁+ t₂
[tex]6.2 = \sqrt{\dfrac{2h}{g}}+\dfrac{h}{343}[/tex]
[tex]6.2 = \sqrt{\dfrac{2h}{9.81}}+\dfrac{h}{343}[/tex]
Now by solving the above equation we get
h= 161.06 m
Therefore the depth of the well will be 161.06 m.
Spiders may "tune" strands of their webs to give an enhanced response at frequencies corresponding to the frequencies at which desirable prey might struggle. Orb web silk has a typical diameter of 0.0020 mm, and spider silk has a density of 1300 kg/m3. To give a resonance at 200Hz to what tension must a spider adjust a 16cm long strand of silk?
To find the tension in the silk strand, we can use the formula: T = (4 x L x f^2 x m x pi^2 x r^2) / (g x rho x sin(theta)). Plugging in the given values, we can solve for T.
Explanation:To find the tension in the silk strand, we can use the formula:
T = (4 x L x f^2 x m x pi^2 x r^2) / (g x rho x sin(theta))
Where:
T is the tension in the strand of silkL is the length of the strand (converted to meters)f is the desired frequency (converted to radians per second)m is the mass per unit length of the silk (density x cross-sectional area)pi is a mathematical constant (approximately 3.14159)r is the radius of the silk strand (half of the diameter)g is the acceleration due to gravity (approximately 9.8 m/s^2)rho is the density of the silktheta is the angle between the strand and the vertical direction (typically 90 degrees)Plugging in the given values:
L = 0.16 mf = 200 Hz (converted to radians per second by multiplying by 2 x pi)m = rho x (pi x r^2)pi = 3.14159r = 0.0010 m (half of the diameter)g = 9.8 m/s^2rho = 1300 kg/m^3theta = 90 degrees (converted to radians by multiplying by pi/180)By substituting these values into the equation and solving for T, we can find the tension in the silk strand.
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The spider must adjust the tension in a 16 cm strand of silk to approximately 0.185 N to achieve a resonance frequency of 200 Hz.
The formula for the fundamental frequency (f) of a stretched string is:
f = (1 / 2L) * √(T / μ)
Where:
f = frequency (200 Hz)L = length of string (0.16 m)T = tension in the string (N)μ = linear mass density (kg/m)First, we calculate the linear mass density (μ) of the spider silk, using:
μ = ρ * A
Where:
ρ = density (1300 kg/m³)A = cross-sectional area (m²)Given the diameter (d) of the strand is 0.0020 mm or 2.0 x 10⁻⁶ m, the cross-sectional area can be calculated as:
A = π * (d / 2)²
A = π * (1.0 x 10⁻⁶)² = π x 10⁻¹² m²
Therefore:
μ = 1300 kg/m³ * π x 10⁻¹² m² = 4.084 x 10⁻⁹ kg/m
Using the frequency formula, rearranged to solve for tension (T):
T = (2Lf)² * μ
T = (2 * 0.16 m * 200 Hz)² * 4.084 x 10⁻⁹ kg/m
T = 184.8272 x 10⁻⁹ N
T ≈ 0.185 N
The tension the spider must adjust to achieve a resonance at 200 Hz for a 16 cm long strand of silk is approximately 0.185 N.
A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision?
a. zero
b. 1500 m/s2
c. 1300 m/s2
d. 200 m/s2
e. 2800 m/s2
Answer:
e. 2800 m/s²
Explanation:
Acceleration: This is the rate of change of velocity. The S.I unit of acceleration is m/s²
Applying Newton's equation of motion,
a = (v-u)/t ................................... Equation 1
Where a = acceleration, v = Final velocity, u = Initial velocity, t = time.
Note: Let the direction of the initial velocity be negative, and the direction of the final velocity be positive
Given: v = 26 m/s, u = -30 m/s, t = 20 ms = 0.02 s
Substitute into equation 1
a = [26-(-30)]/0.02
a = (26+30)/0.02
a = 56/0.02
a = 2800 m/s².
Hence the right option is e. 2800 m/s²
When connected to a battery, a lightbulb glows brightly. If the battery is reversed and reconnected to the bulb, the bulb will glow (a) brighter (b) dimmer (c) with the same brightness (d) not at all
Answer: c) with the same brightness
Explanation: The load in this case the bulb, is not polarized ( it has no positive and negative points) thus any connection relative to the battery (source) will have no effect on it brightness.
Also, brightness is a function of current and in this case the voltage ( from battery) and resistance of load (bulb) is constant, and according to ohms law (V=IR) if the current is constant at the first connection, it will be the same at the reversed connection.
Final answer:
When a battery is reversed and reconnected to a lightbulb, the bulb will glow with the c) same brightness because the alteration does not change the magnitude of the voltage or the resistance in the circuit.
Explanation:
When a battery is reversed and reconnected to a lightbulb, the bulb will glow with the same brightness. This is because the brightness of a bulb in a simple circuit primarily depends on the voltage across the bulb and the resistance in the circuit. Reversing the battery does not change the magnitude of the voltage or the resistance; it merely changes the direction of current flow.
In addition to this, lightbulbs, being resistive elements, respond to the magnitude of the current. As long as the total voltage remains the same, reversing the battery's specific direction does not affect the brightness, thus the correct answer is (c) with the same brightness.
After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube?
Answer:
3.3 m/s
Explanation:
The question is incomplete, here is the complete question:
After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 71 kg and Miranda's is 58 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.
SOLUTION:
mass of Ashley (Ma) = 71 kg
mass of Miranda (Mm) = 58 kg
initial velocity of Ashley (Va) = 2.7 m/s
initial velocity of Miranda (Vm) = 4.1 m/s
Find the final velocity (Vf) at which they both slide together
from the conservation of momentum, initial momentum = final momentum
Ma.Va + Mm.Vm = (Ma + Mm) . Vf
[tex]Vf = \frac{Ma.Va + Mm.Vm}{Ma + Mm} \\ Vf=\frac{(71 x 2.7) + (58 x 4.1)}{71+58}[/tex]
Vf = (191.7 +237.8) / (129)
Vf = 3.3 m/s
0 mph and half the distance at 69.0 mph . On her return trip, she drives half the time at 31.0 mph and half the time at 69.0 mph .
Part AWhat is Julie's average speed on the way to Grandmother's house?
Express your answer with the appropriate units.
Part BWhat is her average speed on the return trip?
Express your answer with the appropriate units.
Answer:
a) v = 34.5 mph, b) v = 50 mph
Explanation:
The average speed is defined.
v = (x₂ -x₁) / (t₂ -t₁)
If the movement is with uniform speed we can also obtain the average speed, averaging the speeds with a time weight factor, if the time is equal for each speed
v = (v₁ + v₂) / 2
a) For the outward journey
v = (69.0 +0) / 2
v = 34.5 mph
b) For the return trip
v = (69.0 + 31.0) / 2
v = 50 mph
If the half-life of an element is about 5,000 years, then a fossil that has one-eighth the normal proportion of the parent isotope to the daughter isotope should be about how many years old?
Answer : The time passed in years is [tex]1.49\times 10^4\text{ years}[/tex]
Explanation :
Half-life = 5000 years
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]k=\frac{0.693}{5000\text{ years}}[/tex]
[tex]k=1.39\times 10^{-4}\text{ years}^{-1}[/tex]
Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = [tex]1.39\times 10^{-4}\text{ years}^{-1}[/tex]
t = time passed by the sample = ?
a = let initial amount of the reactant = X
a - x = amount left after decay process = [tex]\frac{X}{8}[/tex]
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{1.39\times 10^{-4}}\log\frac{X}{(\frac{X}{8})}[/tex]
[tex]t=14962.706\text{ years}=1.49\times 10^4\text{ years}[/tex]
Therefore, the time passed in years is [tex]1.49\times 10^4\text{ years}[/tex]
For a caffeinated drink with a caffeine mass percent of 0.65% and a density of 1.00 g/mL, how many mL of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb?
Explanation:
First we will convert the given mass from lb to kg as follows.
157 lb = [tex]157 lb \times \frac{1 kg}{2.2046 lb}[/tex]
= 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.
[tex]180 \frac{mg}{kg} \times 71.215 kg[/tex]
= 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
0.65% (w/w) = [tex]\frac{0.65 g}{100 g}[/tex]
= [tex]\frac{0.65 g}{(\frac{100 g}{1.0 g/ml})}[/tex]
= [tex]\frac{0.65 g}{100 ml}[/tex]
Therefore, calculate the volume which contains the amount of caffeine as follows.
12818.7 mg = 12.8187 g = [tex]\frac{12.8187 g}{\frac{0.65 g}{100 ml}}[/tex]
= 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.
Which style of jazz music released performers from traditional rules and placed importance on each performer contributing his or her own feelings for the music in the moment? Question 9 options: hard bop jazz fusion free jazz emo jazz
Answer:
The correct answer is: Free Jazz.
Explanation:
Free jazz is a music genre developed around the year 1964 and is considered a subgenre of Jazz where musicians are asked to break the traditional conventions related to the interpretation of jazz music.
In free jazz, the most important technique is improvisation, where musicians simply perform and play their instruments freely.
The key to performing free jazz is to try to express spontaneous feelings through the instrument, while not being aware of certain conventions traditional to jazz music.
In this particular case, to the question Which style of jazz music released performers from traditional rules and placed importance on each performer contributing his or her own feelings for the music in the moment, the correct answer is: Free Jazz.
Calculate the magnitude of the electric field at the center of a square with sides 24.1 cm long if the corners, taken in rotation, have charges of
1.16C,
2.32μC,
3.48μC
4.64μC
(all positive).
Answer:
The net electric field = 1016.96 x 10 raised to power 3 N/C
Explanation:
The detailed steps and mathematical explanation is as shown in the attached file.
A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.66 m/s and a centripetal acceleration :a of magnitude 1.83 m/s2. Position vector :r locates him relative to the rotation axis. (a) What is the magnitude of :r? What is the direction of :r when :a is di- rected (b) due east and (c) due south?
The magnitude of the position vector :r is approximately 7.32 m. When the centripetal acceleration is directed due east, :r will also be due east. When the centripetal acceleration is directed due south, :r will also be due south.
Explanation:The magnitude of the position vector :r can be determined using the equation :a = :v^2 / r where :v is the speed of the man and :a is the centripetal acceleration. Rearranging the equation, we get :r = :v^2 / :a. Substituting the given values, we find :r = (3.66^2) / 1.83 which is approximately 7.32 m.
When the centripetal acceleration is directed due east, the position vector :r will be due east. When the centripetal acceleration is directed due south, the position vector :r will be due south.
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In most energy sources, such as fossil fuels, where is the energy originally derived from?
A. the Sun
B. the Earth's core
C. the magnetic poles
D. the ocean currents
The energy is derived from A.sun.
Explanation:
The energy from sources like Fossil fuels is received from the Producers (Plants, algae) that receives the energy directly from sunlight for photosynthesis earlier long ago. This energy when the plant dies and decomposes over a long period of time and becoming a fossil fuel.Fossils fuels are the remaining of the organisms that lived long back ago they are the energy source for fossil fuel which are burnt in large numbers.Fossil fuels once burnt can never be reused again because their medium gets converted or transferred.Halley's comet moves about the Sun in an elliptical orbit, with its closest approach to the Sun being 0.59 A.U. and its greatest distance being 35 A.U. (A.U. is the Earth-Sun distance). If the comet's speed at closest approach is 47 km/s, what is its speed when it is farthest from the Sun?
Answer:
Explanation:
Given
Halley's closest distance from sun is [tex]r_1=0.59\ A.U.[/tex]
Greatest distance is [tex]r_2=35\ A.U.[/tex]
Comet's speed at closest approach is [tex]v_1=47\ km/s[/tex]
As there is no external torque so angular momentum of comet about the sun is conserved
[tex]L_1=L_2[/tex]
[tex]mr_1^2\times \omega _1=mr_2^2\times \omega _2[/tex]
where [tex]\omega =angular\ velocity [/tex]
This can be written as [tex]\omega =\frac{v}{r}[/tex]
Therefore
[tex]mr_1^2\times \frac{v_1}{r_1}=mr_2^2\times \frac{v_2}{r_2}[/tex]
[tex]r_1\times v_1=r_2\times v_2[/tex]
[tex]0.59\times 47=35\times v_2[/tex]
[tex]v_2=0.79\ km/s[/tex]
A 5.00 kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position is given by y(t)=(2.80 m/s)t +(0.61 m/s^3)t^3.What is the magnitude of the force F when 4.10s ?
Answer: 75.05N
Explanation:
According to newton's second law,
Force = mass×acceleration
Given mass = 5.0kg
Acceleration = change in velocity/time
Velocity = change in displacement/position/time i.e dy/dt
Given position of the particle as y(t)=(2.80 m/s)t +(0.61 m/s)t³
dy/dt = 2.80 + 3(0.61)t²
V = dy/dt = 2.80 + 1.83t²
Acceleration (a) = dv/dt = 2(1.83)t
dv/dt = 3.66t
To get the force when t =4.10second
dv/dt @ t = 4.10s will be 3.66(4.10)
acceleration = 3.66×4.10 = 15.01m/s²
Magnitude of the force F = ma
F = 5.0kg × 15.01m/s²
F = 75.05N
Sarah wanted to find out if temperature has an effect on the growth of bread mold. She grew the mold in nine Petri dishes containing the same amount and type of nutrients. Three were kept at 0 C, three were kept at 90 C, and three were kept at room temperature, 27 C. The containers were examined and the growth of the bread mold was recorded each Friday for five weeks. The dependent or responding variable is:
Answer:
Growth of Bread Mold
Explanation:
The controlled variables are the type of containers used and also the different temperatures.
In Sarah's experiment about the influence of temperature on bread mold, the dependent or responding variable is the growth of bread mold. Her experiment is structured to determine if the mold's growth changes in response to different temperatures.
Explanation:In Sarah's experiment, the dependent or responding variable is the growth of the bread mold. The dependent variable is what changes or responds based on the changes in the independent variable. In this case, Sarah is checking to see if different temperatures (the independent variable) cause different rates of bread mold growth (the dependent variable). An experiment like this can demonstrate how environmental factors, like temperature, affect living organisms such as mold.
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Vector has a magnitude of 4.40 m and is directed east. Vector has a magnitude of 3.40 m and is directed 39.0° west of north. What are (a) the magnitude and (b) the direction (counterclockwise from east) of ? What are (c) the magnitude and (d) the direction (counterclockwise from east) of ?
Answer:
Magnitude = 4.056 m
Direction = 42.3⁰
Explanation:
The vector is resolved in terms of the vertical and horizontal components. Let's look each of these separately.
The vector 4.40 is directed East. This automatically becomes a horizontal component.
But we know that there is a vector 3.40 North West. The angle the vector makes with the horizontal is 61⁰.
Resolving the vectors should yield the horizontal and vertical components:
Horizontal components
The first component is 4.40 m
The second one is derived by resolving 3.40 to the horizontal like this 3.40 × - cos 61⁰ = -1.648 m
Adding the horizontal component gives 4.40 m + ( -1.648 m) = 2.752 m
Vertical components
Resolve 3.40 with the angle 61⁰ like this: vertical comp = 3.41 × sin 61
= 2.98 m
The magnitude is given by √[(2.98)²+ (2.752)²] = 4.056 m Ans
The direction us given by tan⁻¹ (2.98/2.752) = 42.3⁰ Ans
The sound produced by the speakers at a rock concert has a power of 0.181 W. What sound intensity do you hear when you are standing 20.5 m away?
Answer:
The sound intensity heard standing 20.5 m away = 0.0000343 W/m² = 3.43 × 10⁻⁵ W/m²
Explanation:
Intensity of sound at some distance r away is calculated as (power of the sound/surface area of wall of imaginary sphere at distance r)
Power of the sound = 0.181 W
Surface area of wall of imaginary sphere = 4πr² = 4π(20.5²) = 5281.02 m²
Intensity = 0.181/5281.02 = 0.0000343 W/m² = 3.43 × 10⁻⁵ W/m²
If you don't answer this in the next 5 seconds, tomorrow morning you will step on a LEGO trying to grab the milk from the fridge.
Answer:
d = 78 [km]
Explanation:
The displacement shift was from Tipton to Iowa city, so we have:
d1 = 27[km]
Then he travels back for 15[km]
d2 = 15[km]
Finally he returns back to Iowa city the displacement 36 [km]
d3 = 36[km]
d = d1 + d2 + d3
d = 27 + 15 + 36
d = 78 [km]
Racing greyhounds are capable of rounding corners at very high speeds. A typical greyhound track has turns that are 45 m diameter semicircles. A greyhound can run around these turns at a constant speed of 16 m/s .What is its acceleration in m/s^2?What is its acceleration in units of g?
Answer:
In m/s^2:
a=11.3778 m/s^2
In units of g:
a=1.161 g
Explanation:
Since the racing greyhounds are capable of rounding corners at very high speed so we are going use the following formula of acceleration for circular paths.
[tex]a=\frac{v^2}{r}[/tex]
where:
v is the speed
r is the radius
Now,
[tex]a=\frac{16^2}{45/2}\\ a=11.3778 m/s^2[/tex]
In g units:
[tex]a=\frac{11.3778\ g}{9.8}\\ a=1.161\ g[/tex]
Consider the following distinct forces:______________________________.
1.A downward force of gravity.
2.A force exerted by the channel pointing from Q to O.
3.A force in the direction of motion.
4.A force pointing from O to Q.
Which of the above forces is (are) acting on the ball when it is within the frictionless channel at position 'Q'.
n Q?
Answer:
2 and 4
Explanation:
Since it is at a position Q it is stationary ball, for a body to be at a point two opposite forces must act on it
A diver 40 m deep in 10 degrees C fresh water exhales a 1.5 cm diameter bubble.
What is the bubble's diameter just as it reaches the surface of the lake, where the water temperature is 20∘C?
Assume that the air bubble is always in thermal equilibrium with the surrounding water.
Answer:
0.0257259766982 m
Explanation:
[tex]P_2[/tex] = Atmospheric pressure = 101325 Pa
[tex]d_1[/tex] = Initial diameter = 1.5 cm
[tex]d_2[/tex] = Final diameter
[tex]\rho[/tex] = Density of water = 1000 kg/m³
h = Depth = 40 m
The pressure is
[tex]P_1=P_2+\rho gh\\\Rightarrow P_1=101325+1000\times 9.81\times 40\\\Rightarrow P_1=493725\ Pa[/tex]
From ideal gas law we have
[tex]\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\\\Rightarrow \dfrac{P_1\dfrac{4}{3\times8}\pi d_1^3}{T_1}=\dfrac{P_2\dfrac{4}{3\times8}\pi d_2^3}{T_2}\\\Rightarrow \dfrac{P_1d_1^3}{T_1}=\dfrac{P_2d_2^3}{T_2}\\\Rightarrow d_2=(\dfrac{P_1d_1^3T_2}{P_2T_1})^{\dfrac{1}{3}}\\\Rightarrow d_2=(\dfrac{493725\times 0.015^3\times (20+273.15)}{101325\times (10+273.15)})^{\dfrac{1}{3}}\\\Rightarrow d_2=0.0257259766982\ m[/tex]
The diameter of the bubble is 0.0257259766982 m
The function s(t) represents the position of an object at time t moving along a line. Suppose s (2 )equals 146and s (6 )equals 254.Find the average velocity of the object over the interval of time [2 comma 6 ].
Answer:
v(t) = 27 units
Explanation:
The function s(t) represents the position of an object at time t moving along a line such that,
[tex]s(2)=146[/tex]
and
[tex]s(6)=254[/tex]
We need to find the average velocity of the object over the interval of time [2,6]. The velocity of the object is equal to the total distance divided by time. It is given by :
[tex]v(t)=\dfrac{s(6)-s(2)}{6-2}[/tex]
[tex]v(t)=\dfrac{254-146}{6-2}[/tex]
v(t) = 27 units
So, the average velocity of the object is 27 units. Hence, this is the required solution.
An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x-direction, determine her average velocities symbolically for the following. (Assume that time t2 is from the other end of the pool to the starting point. Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only. Indicate the direction with the sign of your answer.)
Answer:
[tex]v_1=\frac{L}{t_1}[/tex]
[tex]v_2=\frac{-L}{t_2}[/tex]
[tex]v_{avg}=\frac{L-L}{t_1+t_2} =0[/tex]
Explanation:
Given:
length of the pool along which the athlete swims, [tex]L[/tex]time taken to swim in the positive x-direction from the start of the pool, [tex]t_1[/tex]time taken to return from the end of the pool to the starting point, [tex]t_2[/tex]Velocity of the athlete from start to the end of the pool in positive direction:
[tex]\rm velocity=\frac{displacement}{time}[/tex]
[tex]v_1=\frac{L}{t_1}[/tex]
Velocity of the athlete from end returning to the start of the pool in negative direction:
Here we have the negative displacement.
[tex]v_2=\frac{-L}{t_2}[/tex]
Now the total average velocity:
[tex]\rm v_{avg}=\frac{total\ displacement}{total\ time}[/tex]
Here we have total displacement as zero because the athlete is finally at the initial starting point.
so,
[tex]v_{avg}=\frac{L-L}{t_1+t_2} =0[/tex]
Final answer:
The symbolic average velocities of an athlete swimming the length of a pool are positive for the trip in one direction (v1 = L / t1) and negative for the return trip (v2 = -L / t2). These reflect the direction of motion related to the positive x-direction.
Explanation:
Average Velocities of an Athlete in a Pool
The average velocity of the athlete for the trip in the positive x-direction is the length of the pool L divided by the time taken t1, which can be symbolically written as v1 = L / t1. Since the swimmer is moving in the positive x-direction, the average velocity v1 is taken as positive.
For the return trip in the negative x-direction, the average velocity is the negative of the length of the pool L divided by the time taken t2, represented as v2 = -L / t2. The average velocity v2 is negative because the swimmer is moving in the opposite direction to the initial positive x-direction.
The concept of average velocity involves both the displacement of the swimmer and the time taken. If, at the end of two trips (to the end of the pool and back), the swimmer's displacement is zero (since they return to the start), the average velocity for the entire trip is also zero.
to prevent a manual-type torch from damage, it is made of a special plastic that resists what?
Answer:
heat
Explanation:
How much kinetic energy is in a runner weighing 83 kg moving at a velocity of 16 m/s
Answer:
10,624J
Explanation:
KE = 1/2 m*v²
KE = 1/2 83*16²
KE = 41.5*256
KE = 10,624J
Technician A says current is the same in each branch of a parallel circuit. Technician B says current is the same everywhere in a series circuit. Who is right?
Answer:
Technician B
Explanation:
The current amp value at the battery position is the current value. The current is the same everywhere for a series circuit without any connecting points. The current at the position of the battery is the same as in each resistor position.
Final answer:
Technician B is correct: current is the same in all parts of a series circuit. Technician A is incorrect: current divides in the branches of a parallel circuit and is not the same. The sum of branch currents equals the total current in parallel circuits.
Explanation:
Understanding Current in Series and Parallel Circuits
Technician B is correct when they say current is the same everywhere in a series circuit. In a series circuit, there is only one path for the current to flow, thus the current (I) is identical through any component in the series, as stated: I = I1 = I2 = I3. This principle is known as the first principle of series circuits. On the other hand, Technician A is incorrect in suggesting current is the same in each branch of a parallel circuit. In parallel circuits, the current divides at each junction and the total supplied current is the sum of the currents in the various branches.
So, in summary, in a series circuit, the current is constant through all components, and the total voltage drop across all components adds up to the voltage supplied by the source. In a parallel circuit, meanwhile, each resistance experiences the same voltage difference, while the current through each branch may vary depending on the resistance of that branch.
Which materials should Hannah choose for her pot and spoon?
A. Hannah should choose copper for her pot because it has the lowest specific heat, and
she should choose wood for her spoon because it has the highest specific heat.
B. Hannah should choose wood for her pot because it has the highest specific heat, and
she should choose copper for her spoon because it has the lowest specific heat.
C. Hannah should choose wood for her pot because it has the highest specific heat, and
she should choose rubber for her spoon because it has the second highest specific
heat.
D. Hannah should choose copper for her pot because it has the lowest specific heat, and
she should choose steel because it has the second lowest specific heat.
A. Hannah should choose copper for her pot because it has the lowest specific heat, and she should choose wood for her spoon because it has the highest specific heat
Explanation:
The specific heat capacity of a substance is the amount of heat required to increase the temperature of 1 kg of the substance by 1 degree.
Mathematically:
[tex]C=\frac{Q}{m\Delta T}[/tex]
where
Q is the amount of heat supplied to the substance
m is the mass of the subtsance
[tex]\Delta T[/tex] is the increase in temperature
This means that:
A substance with higher specific heat needs a lot of energy to raise its temperatureA substance with higher specific heat needs a small amount of energy to increase its temperatureIn this situation, we want:
A material with low specific heat for the pot, because the pot must be able to transmit heat efficiently, so it must be able to become hot (=increase its temperature) with a small amount of heatA material with high specific heat for the spoon, so that the spoon does not become too hot too fast (because it takes a lot of energy to increase its temperature)Therefore, the most reasonable choice in this situation is:
A. Hannah should choose copper for her pot because it has the lowest specific heat, and she should choose wood for her spoon because it has the highest specific heat
Learn more about specific heat:
brainly.com/question/3032746
brainly.com/question/4759369
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You take a bucket outside and hold it as you normally would to hold water. As the rain comes down, the flux of water out of the bucket is Incorrect: Your answer is incorrect. . If you were to then cut out the bottom of the bucket and again hold it in the rain, the flux of water out of the bucket would be (postive, negative, zero) ?
Answer:
the bucket-surface area vector and the direction of the rain is 180° which gives a negative flux in the outward direction.If we cut the base of the bucket then hold it in the rain then the there is no area intercepted by the rainfall and hence we have a zero flux.Explanation:
We know that flux is defined as the density of any energy field passing through a given area parallel to the area vector.
Mathematically:
[tex]\phi=\bar E.A\cos\theta[/tex]
where:
[tex]\phi=[/tex] flux through the area
[tex]A=[/tex] area of concern
[tex]\bar E=[/tex] density of energy field per unit area
[tex]\theta=[/tex] angle between the energy field lines and the normal to area.
When we hold a bucket in the rain then assuming that the base of the bucket is normal to the direction of rainfall then the angle between the area vector and the rain drop is zero when observed from inside.
For the flux outside the bucket we are concerned with the outer surface of the bucket, now the angle formed between the bucket-surface area vector and the direction of the rain is 180° which gives a negative flux in the outward direction.If we cut the base of the bucket then hold it in the rain then the there is no area intercepted by the rainfall and hence we have a zero flux.The angle between the raindrops and the surface area of the bucket is 180 degrees. Hence the flux will be negative and in the outward direction of the bucket.
The value of flux will be zero when the base of the bucket has been cut and then hold in rain.
Electric fluxThe electric flux can be defined as the property of an electric field that shows the number of electric field lines intersecting a given area.
The electric flux can be written in an equation form as given below.
[tex]\phi = EA cos\theta[/tex]
Where [tex]\phi[/tex] is the electric flux, E is the electric field, A is the area of surface and [tex]\theta[/tex] is the angle between the electric field lines and the normal (perpendicular) to A.
Let us consider that the base of the bucket is normal to the direction of the rainfall when we hold the bucket in rain. In this case, the angle between the raindrops and the normal to the surface will be zero inside the bucket.
From the outer surface, the angle formed between the surface area of the bucket and the direction of the rain is 180 degrees. When we put the value of the angle in the formula of flux, we will get a negative flux for the angle of 180 degrees in the outward direction of the bucket.
The flux depends on the surface area. If we cut the base of the bucket and hold it in rain then there will be no surface area that is intersecting by the rainfall. Hence the value of flux will be zero for the no surface area of the bucket.
To know more about the flux, follow the link given below.
https://brainly.com/question/7944455.