# Worksheet: Applications of Derivatives on Rectilinear Motion

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

**Q3: **

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

**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.

**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

**Q13: **

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

**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 particleβs 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