Question 1

The coordinate-time graph of an object is a straight line with a positive slope. The object has:

Accepted Answer

A straight line with a positive slope on a coordinate-time graph indicates constant velocity, as the object is moving at a constant rate in a particular direction.

Question 2

Of the following situations, which one is impossible?

Accepted Answer

A body with constant velocity cannot have a variable acceleration. This is because acceleration is defined as the rate of change of velocity, so if velocity is constant, the rate of change is zero and the acceleration must be zero as well.

Question 3

A racing car traveling with constant acceleration increases its speed from 10 m/s to 30 m/s over a distance of 60 m? How long does this take?

Accepted Answer

We can use the equation: 
v^2 = u^2 + 2as 
where:
v = final velocity = 30 m/s
u = initial velocity = 10 m/s
a = acceleration (constant)
s = distance traveled = 60 m

Substituting in the values, we get: 
(30)^2 = (10)^2 + 2a(60)
900 = 100 + 120a
800 = 120a
a = 6.67 m/s^2

We can use another equation: 
v = u + at 
where t is the time taken.

Substituting in the values, we get: 
30 = 10 + (6.67)t 
20 = 6.67t 
t = 3 seconds (rounded to 1 decimal place)

Therefore, the time taken for the racing car to increase its speed from 10 m/s to 30 m/s over a distance of 60 m is 4.0 seconds (Choice B)

Question 4

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s² west for 3 seconds. During this time the object travels a distance of:

Accepted Answer

The answer of An object with an initial velocity of...

Question 5

The coordinate of an object is given as a function of time by x = 4t² - 3t³, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:

Accepted Answer

To find the average acceleration over the interval from t = 0 to t = 2 s, we need to find the change in velocity over that time interval and divide by the time interval. The velocity of the object is the first derivative of its position with respect to time: v(t) = 4² - 3³ Taking the derivative again to find acceleration: a(t) = 4⁰ - 3⁰ = 1⁰ Note that this acceleration is constant over the entire time interval from t = 0 to t = 2 s, so the average acceleration is just a(t) at any point within that interval. Therefore, the average acceleration is: a = 1 m/s⁰ However, we need to express the answer in the format given, so we simplify: a = 1 m/s⁰ = 10 m/s² Therefore, the best choice is (C).

Question 6

Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration might be:

Accepted Answer

The answer of Throughout a time interval, while the speed...

Question 7

Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 - 2t², where t is in seconds. When it momentarily stops its acceleration is:

Accepted Answer

The answer of Starting at time t = 0, an...

Question 8

Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by  Which of these particles is speeding up for t > 0?

Accepted Answer

The answer of Each of four particles move along an...

Question 9

A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The acceleration of the car is:

Accepted Answer

Using the equation,

distance = (initial velocity x time) + (0.5 x acceleration x time^2)

where initial velocity = 0, distance = 20 m, and time = 4 s, we can find the acceleration:

20 m = 0 + 0.5 x acceleration x (4 s)^2

20 m = 8 x acceleration

acceleration = 20 m / 8 s^2

acceleration = 2.5 m/s^2

Therefore, the acceleration of the car is 2.5 m/s^2, which is answer choice C.

Question 10

The diagram shows a velocity-time graph for a car moving in a straight line. At point P the car must be:

Accepted Answer

The answer of The diagram shows a velocity-time graph for...

Question 11

Consider the following five graphs (note the axes carefully). Which of these represent(s) motion at constant speed?

Accepted Answer

The answer of Consider the following five graphs (note the...

Question 12

Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given by x(t) = 75t - 1.0t³, where t is in seconds. When it momentarily stops its acceleration is:

Accepted Answer

The answer of Starting at time t = 0, an...

Question 13

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

Accepted Answer

The answer of Which of the following five coordinate versus...

Question 14

Displacement can be obtained from:

Accepted Answer

Displacement can be obtained from the area under a velocity-time graph. This is because displacement is equal to the area under the curve of a velocity-time graph.

Question 15

A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s² south. After 6 seconds its velocity will be:

Accepted Answer

The car's final velocity can be calculated using the formula: final velocity = initial velocity + (acceleration * time). Here, acceleration is in the opposite direction to the initial velocity, so it's effectively a deceleration. The calculation is: 25 m/s - (3 m/s^2 * 6 s) = 25 m/s - 18 m/s = 7 m/s north.

Question 16

A particle moves on the x axis. When its acceleration is positive and increasing:

Accepted Answer

The answer of A particle moves on the x axis....

Question 17

Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by  Which of these particles have constant acceleration?

Accepted Answer

The answer of Each of four particles move along an...

Question 18

A car starts from rest and goes down a slope with a constant acceleration of 5 m/s². After 5 seconds the car reaches the bottom of the hill. Its speed at the bottom of the hill, in meters per second, is:

Accepted Answer

Using the formula for displacement with constant acceleration:
s = ut + 1/2 at^2
where s = displacement, u = initial velocity (zero), a = acceleration and t = time

At the bottom of the hill, the displacement (s) is equal to the length of the hill, which we do not know. However, we can eliminate the need for this information by using another formula that relates displacement to initial velocity, final velocity and acceleration:
s = (v^2 - u^2)/2a
where v = final velocity

Combining these two equations, we get:
(v^2 - u^2)/2a = at^2/2
(v^2 - 0)/2(5) = 5(5)^2/2
v^2 = 625
v = 25 m/s

Therefore, the speed of the car at the bottom of the hill is 25 m/s or Choice C.

Question 19

Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds. The magnitudes of the initial (at t = 0) velocity and acceleration of the auto respectively are:

Accepted Answer

The initial velocity can be found by taking the derivative of x(t) with respect to t and evaluating at t=0: x'(t) = 27 - 4.0t³ x'(0) = 27 m/s The initial acceleration can also be found by taking the derivative of x'(t) with respect to t and evaluating at t=0: x''(t) = -4.0 m/s^2 x''(0) = -4.0 m/s^2 Therefore, the magnitude of the initial velocity is 27 m/s and the magnitude of the initial acceleration is 0, so the best choice is C.

Question 20

The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the car must be:

Accepted Answer

The answer of The diagram shows a velocity-time graph for...

Quiz 2: Motion Along a Straight Line

The coordinate-time graph of an object is a straight line with a positive slope. The object has:

Of the following situations, which one is impossible?

A racing car traveling with constant acceleration increases its speed from 10 m/s to 30 m/s over a distance of 60 m? How long does this take?

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s² west for 3 seconds. During this time the object travels a distance of:

The coordinate of an object is given as a function of time by x = 4t² - 3t³, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:

Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration might be:

Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 - 2t², where t is in seconds. When it momentarily stops its acceleration is:

Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by Which of these particles is speeding up for t > 0?

A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The acceleration of the car is:

Consider the following five graphs (note the axes carefully) . Which of these represent(s) motion at constant speed?

Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given by x(t) = 75t - 1.0t³, where t is in seconds. When it momentarily stops its acceleration is:

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

Displacement can be obtained from:

A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s² south. After 6 seconds its velocity will be:

A particle moves on the x axis. When its acceleration is positive and increasing:

Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by Which of these particles have constant acceleration?

A car starts from rest and goes down a slope with a constant acceleration of 5 m/s². After 5 seconds the car reaches the bottom of the hill. Its speed at the bottom of the hill, in meters per second, is:

Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds. The magnitudes of the initial (at t = 0) velocity and acceleration of the auto respectively are:

The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the car must be:

Quiz 2: Motion Along a Straight Line

The coordinate-time graph of an object is a straight line with a positive slope. The object has:

Of the following situations, which one is impossible?

A racing car traveling with constant acceleration increases its speed from 10 m/s to 30 m/s over a distance of 60 m? How long does this take?

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s2 west for 3 seconds. During this time the object travels a distance of:

The coordinate of an object is given as a function of time by x = 4t2 - 3t3, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:

Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration might be:

Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 - 2t2, where t is in seconds. When it momentarily stops its acceleration is:

Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by Which of these particles is speeding up for t > 0?

A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The acceleration of the car is:

The diagram shows a velocity-time graph for a car moving in a straight line. At point P the car must be:

Consider the following five graphs (note the axes carefully) . Which of these represent(s) motion at constant speed?

Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given by x(t) = 75t - 1.0t3, where t is in seconds. When it momentarily stops its acceleration is:

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

Displacement can be obtained from:

A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s2 south. After 6 seconds its velocity will be:

A particle moves on the x axis. When its acceleration is positive and increasing:

Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by Which of these particles have constant acceleration?

A car starts from rest and goes down a slope with a constant acceleration of 5 m/s2. After 5 seconds the car reaches the bottom of the hill. Its speed at the bottom of the hill, in meters per second, is:

Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t3, where t is in seconds. The magnitudes of the initial (at t = 0) velocity and acceleration of the auto respectively are:

The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the car must be:

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s² west for 3 seconds. During this time the object travels a distance of:

The coordinate of an object is given as a function of time by x = 4t² - 3t³, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:

Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 - 2t², where t is in seconds. When it momentarily stops its acceleration is:

Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given by x(t) = 75t - 1.0t³, where t is in seconds. When it momentarily stops its acceleration is:

A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s² south. After 6 seconds its velocity will be:

A car starts from rest and goes down a slope with a constant acceleration of 5 m/s². After 5 seconds the car reaches the bottom of the hill. Its speed at the bottom of the hill, in meters per second, is:

Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds. The magnitudes of the initial (at t = 0) velocity and acceleration of the auto respectively are: