# 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.

**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 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

**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 .

**Q9: **

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.