# 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 .

**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 particleβs velocity is zero, its acceleration is m/s^{2}. 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

**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.