# Lesson Worksheet: Applications of Derivatives on Rectilinear Motion Mathematics • Higher Education

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 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.

Q2:

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

• BAccelerating

Q3:

A particle is moving in a straight line along the such that its displacement meters after seconds is given by . Find the maximum velocity of the particle in the positive -direction.

Q4:

A particle moves along the . Its position from the origin is meters at a time seconds. The position is given by the equation . Find the times at which the particleβ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

Q5:

A particle is moving in a straight line such that its displacement meters after seconds is given by .

Find the velocity of the particle at .

Find the time interval during which the velocity of the particle is decreasing.

• A
• B
• C
• D
• E

Q6:

A particle is moving in a straight line such that its displacement at time is given by .

What is the total distance covered by the particle during the first 2 seconds? Write your answer approximate to two decimal places.

Q7:

A particle moves in a straight line, with respect to a stationary point, with position vector , where and is measured in seconds. is a unit vector parallel to the straight line, and is measured in meters.

Find the magnitude of the displacement vector after 2 s.

Find the total distance covered by the particle after 2 s.

Determine the magnitude of the average velocity vector of the particle between and .

Determine the average speed of the particle between and .

Q8:

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

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

Q9:

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

Q10:

A particle moves along the . When its displacement from the origin is m, its velocity is given by Find the particleβs minimum velocity.

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