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

**Q2: **

A particle is moving in a straight line such that its position meters relative to the origin at time seconds is given by Find the particleβs average velocity between and .

- A 18 m/s
- B 11 m/s
- C m/s
- D 9 m/s

**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 .

**Q4: **

A particle moves along the -axis such that at time seconds, its displacement from the origin is given by What is the particleβs average velocity in the first 10 seconds?

**Q5: **

A particle is moving in a straight line such that its displacement in metres is given as a function of time in seconds by Find the magnitude of the acceleration of the particle when the velocity is zero.

**Q6: **

A particle moves along the -axis. At time
seconds, its displacement from the origin is given by
Determine the time at which the particleβs acceleration is 9 m/s^{2}.

- A s
- B 3 s
- C s
- D s
- E s

**Q7: **

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

- Aaccelerating
- Bdecelerating

**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
- B27, 25
- C12, 10
- 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

**Q12: **

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

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q13: **

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