# Lesson Worksheet: Linear Motion with Derivatives Mathematics

In this worksheet, we will practice using differentiation to find instantaneous velocity, speed, and acceleration of a particle.

Q1:

A particle started moving along the -axis. At time seconds, its position relative to the origin is given by Find the maximum distance between the particle and the origin , and determine the velocity of the particle when .

• A,
• B,
• C,
• D,

Q2:

A particle moves along the -axis such that at time seconds its displacement from the origin is given by Determine the particle’s acceleration when .

Q3:

A particle moves along the -axis so that its position relative to the origin after time (where ) is given by What is the particle’s maximum displacement?

Q4:

A stone is projected vertically upward. At time seconds, its height from the ground is given by Determine the speed of the stone when it is 22.5 m high.

Q5:

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

Q6:

A particle is moving in a straight line such that its displacement after seconds is given by Determine the time after which the particle changes its direction.

Q7:

A particle moving along a path has velocity and acceleration . Given that the equation of the displacement is , find .

• A
• B
• C
• D

Q8:

A particle moves along the . At time seconds, its displacement from the origin is given by Determine all the possible values of , in seconds, at which the particle’s speed m/s.

• A2, 10
• B, 2
• C1, 5
• D, 1
• E,

Q9:

A particle moves along the such that at time seconds its displacement from the origin is given by Find the particle’s velocity, , and acceleration, , at .

• A,
• B,
• C,
• D,
• E,

Q10:

A particle is moving in a straight line. After time seconds, where , the body’s displacement relative to a fixed point is given by , where is a fixed unit vector. Find the initial velocity of the particle and its acceleration ,  5 seconds after it started moving.

• A,
• B,
• C,
• D,

This lesson includes 17 additional questions and 171 additional question variations for subscribers.