# Worksheet: Applications of Derivatives on Rectilinear Motion

In this worksheet, we will practice applying derivatives to problems of motion in a straight line.

Q1:

A particle is moving in a straight line such that its displacement after seconds is given by Determine the time interval during which the velocity of the particle is increasing.

• A
• B
• C
• D

Q2:

A particle is moving in a straight line such that its position meters relative to the origin at time seconds is given by Find the particle’s average velocity between and .

• A18 m/s
• B11 m/s
• C m/s
• D9 m/s

Q3:

A particle started moving along the -axis. At time seconds, the its displacement from the origin is given by Find the body’s average speed within the time interval .

Q4:

A particle moves along the -axis such that at time seconds, its displacement from the origin is given by What is the particle’s average velocity in the first 10 seconds?

Q5:

A particle is moving in a straight line such that its displacement in meters is given as a function of time in seconds by . Find the magnitude of the acceleration of the particle when the velocity is zero.

Q6:

A particle moves along the -axis. At time seconds, its displacement from the origin is given by Determine the time at which the particle’s acceleration is 9 m/s2.

• A s
• B s
• C s
• D s
• E3 s

Q7:

A particle moves in a straight line such that at time seconds its displacement from a fixed point on the line is given by Determine whether the particle is accelerating or decelerating when .

• Baccelerating

Q8:

A body moves along the -axis such that at time seconds, its displacement from the origin is given by What is its velocity when its acceleration is equal to 0?

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q9:

A particle is moving in a straight line such that its displacement at seconds is given by Find the velocity of the particle when the acceleration is zero.

Q10:

A particle is moving in a straight line such that its displacement in meters, , after seconds is given by . When the particle’s velocity is zero, its acceleration is m/s2. Find all the possible values of .

• A24, 22
• B12, 10
• C27, 25
• D, 12

Q11:

A particle moves along the -axis such that at time seconds () its velocity is given by . Determine the time interval in which the particle decelerates.

• A
• B
• C
• D
• E

Q12:

A particle moves along the -axis. When its displacement from the origin is m, its velocity is given by Find the particle’s acceleration when .

• A m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

Q13:

A particle started moving along the -axis. When the particle’s displacement from the origin is meters, its velocity is given by . Find the particle’s acceleration when its velocity vanished.

Q14:

A particle moves along the . Its velocity, , in meters per second is given by , where is the time in seconds. Find the interval over which the particle is accelerating in the positive -direction.

• A
• B
• C
• D
• E

Q15:

A particle moves along the . Its displacement from the origin is meters at a time seconds. The displacement is given by the equation . Find the times at which the particle’s velocity is equal to 0.

• A, where is an integer
• B, where is an integer
• C, where is an integer
• D, where is an integer
• E, where is an integer