Question 1

The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?

Accepted Answer

The answer of The figure represents the position of a...

Question 2

Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of 3.0 m/s and Betty has a speed of 2.0 m/s. Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run?

Accepted Answer

The answer of Arthur and Betty start walking toward each...

Question 3

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object? A) -12.0 m/s² B) 24.0 m/s² C) -4.00 m/s² D) 4.00 m/s² E) 8.00 m/s²

Accepted Answer

The answer of An object starts from rest at time...

Question 4

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s,
(a) what is the average speed of the object?
(b) what is the average velocity of the object?

Accepted Answer

The answer of The figure shows the position of an...

Question 5

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 5.00 s. A) -8.00 m/s² B) -7.00 m/s² C) 2.00 m/s² D) 0.00 m/s² E) -2.00 m/s²

Accepted Answer

The instantaneous acceleration can be found by taking the derivative of the velocity function with respect to time: a(t) = dv/dt = 3.00 m/s - 2(1.0 m/s²) t At time t = 5.00 s, we have: a(5.00) = 3.00 m/s - 2(1.0 m/s²) (5.00 s) a(5.00) = 3.00 m/s - 10.00 m/s² a(5.00) = -7.00 m/s² Therefore, the instantaneous acceleration at time t = 5.00 s is -7.00 m/s², which corresponds to choice B.

Question 6

A airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane? A) 4.44 m/s² B) 2.45 m/s² C) 7.33 m/s² D) 5.78 m/s² E) 1.34 m/s²

Accepted Answer

We can use the formula vf^2 = vi^2 + 2ad, where vf = final velocity, vi = initial velocity, a = acceleration, and d = distance traveled. Rearranging this equation to solve for acceleration, we get a = (vf^2 - vi^2) / 2d. Plugging in the given values, we get a = ((2.40 × 10^10)^2 - (2.00 × 10^10)^2) / (2 × 1.20 × 10^3) = 7.33 m/s^2. Therefore, the answer is C.

Question 7

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³)t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s? A) 18.0 m/s B) 54.0 m/s C) 0.00 m/s D) 15.0 m/s E) 108 m/s

Accepted Answer

To find the velocity at time t=6s, we need to integrate the acceleration function from 0s to 6s:
v(t) = ∫[0,6] a(t) dt = ∫[0,6] (3.00t) dt
v(t) = 1.5t^2 + C   (where C is the constant of integration)
Since the object is at rest at t=0, we know that the initial velocity is 0 m/s. Therefore, we can solve for C:
0 = 1.5(0)^2 + C 
C = 0 
Thus the velocity function is: v(t) = 1.5t^2 
The velocity at t=6s is:
v(6) = 1.5(6)^2 = 54.0 m/s
Therefore, the correct answer is B.

Question 8

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s³)t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time T = 0.000 s. A) (4.00 m/s)t + 1.00 m B) (3.00 m/s)t + (1.33 m/s3)t³ C) (4.00 m/s)t D) 1.33 m E) 1.00 m + (3.00 m/s)t + (1.33 m/s³)t³

Accepted Answer

To find the position of the object as a function of time, we need to integrate the velocity function with respect to time. 
∫v(t) dt = ∫(3.00 m/s + (4.00 m/s^2)t) dt
= 3.00t + (2.00 m/s^2)t^2 + C
where C is the constant of integration. To find C, we use the initial condition that the object is located at x = 1.00 m at time t = 0.00 s: 
1.00 m = 3.00(0.00) + (2.00 m/s^2)(0.00)^2 + C
C = 1.00 m
So, the position function is: 
x(t) = 3.00t + (2.00 m/s^2)t^2 + 1.00 m
Rearranging and simplifying, we get: 
x(t) = 1.00 m + (3.00 m/s)t + (2.00 m/s^2)t^2
Using the identity 2a + b = (a+b)^2 - (a-b)^2 with a = 1.33 m/s^2 and b = 3.00 m/s, we can write: 
x(t) = 1.00 m + (3.00 m/s)t + (1.33 m/s^2)t^2 + (3.00 m/s)(1.33 m/s^2)t^3
= 1.00 m + (3.00 m/s)t + (1.33 m/s^3)t^3
Therefore, the best choice is E.

Question 9

The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. for the 10 s shown on the graph, find
(a) the net displacement of the player.
(b) the total distance run by the player.

Accepted Answer

The answer of The figure shows a graph of the...

Question 10

A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?
A) 6.67 s
B) 15.0 s
C) 9.80 s
D) 10.2 s
E) 13.3 s

Accepted Answer

The answer of A runner maintains constant acceleration after starting...

Question 11

The figure shows the position of an object as a function of time. During the time interval from time
t = 0.0 s and time t = 9.0 s,
(a) what is the length of the path the object followed?
(b) what is the displacement of the object?

Accepted Answer

The answer of The figure shows the position of an...

Question 12

The position of an object is given by where And x and t are in SI units. What is the instantaneous acceleration of the object when A) -13 m/s² B) 2.9 m/s² C) 4.6 m/s² D) 13 m/s²

Accepted Answer

The answer of The position of an object is given...

Question 13

The position of an object as a function of time is given by x =bt² - ct, where b = 2.0 m/s² and C = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2? A) 1.7 m/s B) 2.1 m/s C) 2.3 m/s D) 2.7 m/s

Accepted Answer

The answer of The position of an object as a...

Question 14

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s². How far does the car travel while accelerating? A) 80.0 m B) 133 m C) 226 m D) 399 m

Accepted Answer

The answer of A car accelerates from 10.0 m/s to...

Question 15

A cat runs along a straight line (the x-axis) from point A to point B to point C, as shown in the figure. The distance between points A and C is 5.00 m, the distance between points B and C is 10.0 m, and the positive direction of the x-axis points to the right. The time to run from A to B is 20.0 s, and the time from B to C is 8.00 s. As the cat runs along the x-axis between points A and C
(a) what is the magnitude of its average velocity?
(b) what is its average speed?

Accepted Answer

The answer of A cat runs along a straight line...

Question 16

If the fastest you can safely drive is 65 mi/h what is the longest time you can stop for dinner if you must travel 541 m in 9,6 h total?
A) 1.0 h
B) 1.3 h
C) 1.4 h
D) You can't stop at all.

Accepted Answer

To find the longest time you can stop, first we need to calculate the maximum distance you can travel in 9.6 hours. 
Distance= Speed x Time 
Maximum distance= 65 mi/h x 9.6 h= 624 miles

Now subtract the distance traveled from the maximum distance to find the distance you can cover while stopping for dinner:

Distance while stopping= 624 miles - 541 miles= 83 miles

To find the maximum time you can stop, divide the distance while stopping by the maximum speed:

Time= Distance/ Speed 
Time= 83 mi/ 65 mi/h= 1.3 hours

Therefore, the correct answer is B) 1.3 h.

Question 17

The position of an object as a function of time is given by  
where  
  
c = 60 m/s and d = 7.0 m.
(a) Find the instantaneous acceleration at t =2.4 s.
(b) Find the average acceleration over the first 2.4 seconds.

Accepted Answer

The answer of The position of an object as a...

Question 18

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³)t, where t is in seconds. If the object has a velocity 1.00 m/s at time t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s? A) 33.0 m B) 30.0 m C) 36.0 m D) 27.0 m

Accepted Answer

The answer of The acceleration of an object as a...

Question 19

A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h? 
A) Before marker 1
B) At marker 1
C) Between marker 1 and marker 2

Accepted Answer

The answer of A racing car accelerates uniformly from rest...

Question 20

A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?
A) 296 mi/h
B) 269 mi/h
C) 188 mi/h
D) 135 mi/h

Accepted Answer

First, we need to determine the acceleration:
a = (2 * d) / t^2
where d is the distance (1/4 mile) and t is the time (6.70 s)
a = (2 * 1/4) / (6.70)^2
a = 0.124 mi/s^2

Next, we can use the equation:
v = at
where v is the final velocity and a is the acceleration found above, and t is the time it took to travel the distance. We convert 1/4 mile to feet:
1/4 mile = 1320 feet / 4 = 330 feet
t = 6.70 s
v = (0.124 mi/s^2) * (6.70 s) = 0.83 mi/s = 1384 ft/s

Finally, we convert feet per second to miles per hour:
1384 ft/s * (3600 s/hour) / (5280 ft/mile) = 942.8 mi/h
We round this to the nearest 5 mi/h to get:
Answer: B) 269 mi/h

Quiz 2: Kinematics in One Dimension

The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s, (a) what is the average speed of the object? (b) what is the average velocity of the object?

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 5.00 s.

A airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s³) t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time T = 0.000 s.

The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. for the 10 s shown on the graph, find (a) the net displacement of the player. (b) the total distance run by the player.

A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?

The figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s, (a) what is the length of the path the object followed? (b) what is the displacement of the object?

The position of an object is given by where And x and t are in SI units. What is the instantaneous acceleration of the object when

The position of an object as a function of time is given by x =bt² - ct, where b = 2.0 m/s² and C = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2?

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s². How far does the car travel while accelerating?

If the fastest you can safely drive is 65 mi/h what is the longest time you can stop for dinner if you must travel 541 m in 9,6 h total?

The position of an object as a function of time is given by where c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object has a velocity 1.00 m/s at time t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h?

A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?

Quiz 2: Kinematics in One Dimension

The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s, (a) what is the average speed of the object? (b) what is the average velocity of the object?

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s2) t2. Determine the instantaneous acceleration of the object at time t = 5.00 s.

A airplane that is flying level needs to accelerate from a speed of 2.00 × 102 m/s to a speed of 2.40 × 102 m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3) t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s3) t2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time T = 0.000 s.

The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. for the 10 s shown on the graph, find (a) the net displacement of the player. (b) the total distance run by the player.

A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?

The figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s, (a) what is the length of the path the object followed? (b) what is the displacement of the object?

The position of an object is given by where And x and t are in SI units. What is the instantaneous acceleration of the object when

The position of an object as a function of time is given by x =bt2 - ct, where b = 2.0 m/s2 and C = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2?

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s2. How far does the car travel while accelerating?

If the fastest you can safely drive is 65 mi/h what is the longest time you can stop for dinner if you must travel 541 m in 9,6 h total?

The position of an object as a function of time is given by where c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3) t, where t is in seconds. If the object has a velocity 1.00 m/s at time t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h?

A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 5.00 s.

A airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s³) t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time T = 0.000 s.

The position of an object as a function of time is given by x =bt² - ct, where b = 2.0 m/s² and C = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2?

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s². How far does the car travel while accelerating?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object has a velocity 1.00 m/s at time t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?