Question 1

A particle moves on the x axis.When its acceleration is positive and increasing:
A)its velocity must be positive
B)its velocity must be negative
C)it must be slowing down
D)it must be speeding up
E)none of the above must be true

Accepted Answer

A positive and increasing acceleration does not necessarily dictate the direction or change in speed of the velocity. The velocity could be positive or negative, and the particle could be speeding up or slowing down depending on its initial velocity and the rate of acceleration.

Question 2

The diagram shows a velocity-time graph for a car moving in a straight line.At point P the car must be: 
A)moving with zero acceleration
B)climbing the hill
C)accelerating
D)stationary
E)moving at about 45° with respect to the x axis

Accepted Answer

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

Question 3

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: A)0 m/s; 12 m/s² B)0 m/s; 24 m/s² C)27 m/s; 0 m/s² D)27 m/s; 12 m/s² E)27 m/s; 24 m/s²

Accepted Answer

The answer of Over a short interval, starting at time...

Question 4

A ball rolls up a slope.At the end of three seconds its velocity is 20 cm/s; at the end of eight seconds its velocity is 0 cm/s.What is the magnitude of its average acceleration from the third to the eighth second? A)2.5 cm/s² B)4.0 cm/s² C)5.0 cm/s² D)6.0 cm/s² E)6.67 cm/s²

Accepted Answer

The answer of A ball rolls up a slope.At the...

Question 5

Can an object have positive acceleration and decreasing speed?
A)No, this is not possible.
B)Yes, speed will always decrease if acceleration is positive.
C)Yes, this is possible if the initial velocity is zero.
D)Yes, this is possible if the initial velocity is negative.
E)Yes, this is possible but only if the object is moving in two dimensions.

Accepted Answer

If an object has a negative initial velocity and positive acceleration, then the speed will decrease even though the acceleration is positive. This is because the positive acceleration is only slowing down the negative initial velocity, eventually bringing the object to a stop and possibly even reversing its direction.

Question 6

What is the relationship between instantaneous speed and instantaneous velocity?
A)They are identical.
B)Instantaneous speed is the rate at which the instantaneous velocity is changing.
C)Instantaneous speed is the magnitude of the instantaneous velocity.
D)They are unrelated.
E)Instantaneous speed is the initial speed minus the final speed.

Accepted Answer

Instantaneous speed is the magnitude of the instantaneous velocity, which means they have the same magnitude (or numerical value). However, velocity is a vector quantity that includes the direction of motion, while speed is a scalar quantity that only describes the magnitude of motion.

Question 7

Which of the following five acceleration versus time graphs is correct for an object moving in a straight line at a constant velocity of 20 m/s? 
A)I
B)II
C)III
D)IV
E)V

Accepted Answer

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

Question 8

A particle moves along the x axis according to the equation x = 6t² where x is in meters and t is in seconds.Therefore: A)the acceleration of the particle is 6 m/s² B)t cannot be negative C)the particle follows a parabolic path D)each second the velocity of the particle changes by 9.8 m/s E)none of the above

Accepted Answer

The equation provided, x = 6t, suggests a linear relationship between position x and time t, indicating constant velocity, not acceleration or a parabolic path. The equation does not imply that t cannot be negative, as negative time values could represent times before a chosen starting point. The equation also does not specify a change in velocity of 9.8 m/s each second, which is the acceleration due to gravity and unrelated to the given equation.

Question 9

Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t)= 27t - 4.0t³, where t is in seconds.At the end of 1.0 s the acceleration of the auto is: A)23 m/s² B)15 m/s² C)-4.0 m/s² D)-12 m/s² E)-24 m/s²

Accepted Answer

The acceleration is the second derivative of the position function x(t). Differentiating x(t) = 27t - 4.0t^3 twice gives a(t) = -24t. At t = 1.0 s, a(1) = -24(1) = -24 m/s².

Question 10

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: A)-8 m/s² B)4 m/s² C)-10 m/s² D)10 m/s² E)-13 m/s²

Accepted Answer

To find the average acceleration over the time interval from t = 0 to t = 2 s, we need to find the change in velocity over that interval and divide by the time interval. The velocity at any time t is the derivative of the position function with respect to time: v = dx/dt = 4² - 3³ So the change in velocity over the interval from t = 0 to t = 2 s is: Δv = v(2) - v(0) = (4² - 3³) - (4⁰ - 3⁰) = 4² - 3² = ² So the average acceleration is: a = Δv/Δt = (²)/(2 - 0) = -10 m/s². Therefore, the answer is (C), -10 m/s².

Question 11

The diagram shows a velocity-time graph for a car moving in a straight line.At point Q the car must be: 
A)moving with zero acceleration
B)traveling downhill
C)traveling below ground-level
D)reducing speed
E)traveling in the reverse direction to that at point P

Accepted Answer

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

Question 12

A car accelerates from rest on a straight road.A short time later, the car decelerates to a stop and then returns to its original position in a similar manner, by speeding up and then slowing to a stop.Which of the following five coordinate versus time graphs best describes the motion? 
A)I
B)II
C)III
D)IV
E)V

Accepted Answer

The answer of A car accelerates from rest on a...

Question 13

Of the following situations, which one is impossible?
A)A body having velocity east and acceleration east
B)A body having velocity east and acceleration west
C)A body having zero velocity and non-zero acceleration
D)A body having constant acceleration and variable velocity
E)A body having constant velocity and variable acceleration

Accepted Answer

A body with constant velocity cannot have variable acceleration because acceleration is the change in velocity over time. If velocity is constant, there is no change, and thus acceleration must also be constant or zero, making variable acceleration impossible.

Question 14

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: A)0 m/s² B)-4.0 m/s² C)-9.8 m/s² D)-28 m/s² E)49 m/s²

Accepted Answer

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

Question 15

Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration could be:
A)positive and negative, respectively
B)negative and positive, respectively
C)negative and negative, respectively
D)negative and zero, respectively
E)positive and zero, respectively

Accepted Answer

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

Question 16

The diagram represents the straight line motion of a car.Which of the following statements is true? A)The car's speed increases, then it stops, and reverses B)The car accelerates at 6 m/s² for the first 2 s C)The car is moving for a total time of 12 s D)The car accelerates at -12 m/s² for the last 4 s E)The car returns to its starting point when t = 9 s

Accepted Answer

The diagram shows a straight line motion, and the slope of the line is equal to the velocity of the car. The slope of the line in the first 2 seconds is 6 m/s, indicating that the car is accelerating at a rate of 6 m/s². Therefore, option B is true. Option A and D are false, as there is no evidence of the car stopping or reversing, or accelerating at -12 m/s² in the last 4 seconds. Option C is also false, as the motion lasts for 9 seconds, not 12. Option E is also false, as there is no evidence that the car returns to its starting point.

Question 17

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)0 m/s² B)-73 m/s² C)-30 m/s² D)-9.8 m/s² E)9.2 x 10³ m/s²

Accepted Answer

The object momentarily stops when its velocity is zero. The velocity is the derivative of the position function: v(t) = 75 - 3t^2. Setting v(t) = 0 gives t = 5 seconds. The acceleration is the derivative of the velocity: a(t) = -6t. At t = 5 seconds, a(5) = -30 m/s².

Question 18

All falling objects experience some air resistance, the effect of which is to decrease acceleration.When the falling object's acceleration reaches zero, the acceleration stops changing.Therefore, if you drop an object and it falls far enough for this to happen,
A)its speed continues to increase all the way down.
B)its speed reaches a maximum value and then decreases.
C)its speed reaches a maximum value and then doesn't change.
D)its speed reaches a maximum value, decreases, and then increases again.
E)Any of these things could happen.

Accepted Answer

When an object falls through the air and its acceleration reaches zero due to air resistance, it has achieved terminal velocity. At this point, its speed remains constant, reaching a maximum value that does not change as it continues to fall.

Question 19

Each of four particles moves 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)All four
B)Only 1 and 2
C)Only 2 and 3
D)Only 3 and 4
E)None of them

Accepted Answer

We can determine the acceleration of each particle by taking the second derivative of its position function with respect to time.

Particle 1: a(t) = 0.2
Particle 2: a(t) = -0.3
Particle 3: a(t) = 0
Particle 4: a(t) = -0.1

Particles with constant acceleration would have a constant second derivative, which means their acceleration would not change over time. Therefore, the only particles with constant acceleration are those with a(t) = 0 or a constant non-zero value.

Particles 2 and 3 have constant acceleration, while particles 1 and 4 do not. Therefore, the answer is D, only particles 3 and 4 have constant acceleration.

Question 20

Is it possible for an object to have zero velocity and constant nonzero acceleration?
A)Yes, but only if it is not moving at all.
B)No, if its velocity is zero its acceleration must also be zero.
C)Yes, all objects with zero velocity have nonzero acceleration.
D)No, if its acceleration is not zero its velocity cannot be zero.
E)Yes, but its velocity must only be zero for an instant.

Accepted Answer

It is possible for an object to have zero velocity and constant nonzero acceleration if its velocity is zero for an instant, but then changes to a non-zero velocity due to the constant non-zero acceleration. This can be seen in situations such as an object thrown vertically upwards where its velocity is momentarily zero at the highest point of its trajectory before it starts falling back down due to the constant acceleration of gravity.

Quiz 2: Motion Along a Straight Line

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

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

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:

A ball rolls up a slope.At the end of three seconds its velocity is 20 cm/s; at the end of eight seconds its velocity is 0 cm/s.What is the magnitude of its average acceleration from the third to the eighth second?

Can an object have positive acceleration and decreasing speed?

What is the relationship between instantaneous speed and instantaneous velocity?

Which of the following five acceleration versus time graphs is correct for an object moving in a straight line at a constant velocity of 20 m/s?

A particle moves along the x axis according to the equation x = 6t² where x is in meters and t is in seconds.Therefore:

Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds.At the end of 1.0 s the acceleration of the auto is:

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:

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

A car accelerates from rest on a straight road.A short time later, the car decelerates to a stop and then returns to its original position in a similar manner, by speeding up and then slowing to a stop.Which of the following five coordinate versus time graphs best describes the motion?

Of the following situations, which one is impossible?

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:

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

The diagram represents the straight line motion of a car.Which of the following statements is true?

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:

All falling objects experience some air resistance, the effect of which is to decrease acceleration.When the falling object's acceleration reaches zero, the acceleration stops changing.Therefore, if you drop an object and it falls far enough for this to happen,

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

Is it possible for an object to have zero velocity and constant nonzero acceleration?