**Q3: **

The acceleration of a particle moving in a straight line, at time seconds, is given by When , the particle moves with uniform velocity . Determine the velocity and the distance, , covered by the particle in the first 23 s of motion.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q4: **

A body started moving along the -axis
from the origin at an initial speed of 10 m/s.
When it was meters away from the origin and moving at
m/s,
its acceleration was m/s^{2}
in the direction of increasing .
Determine when .

- A m
- B m
- C m
- D m
- E m

**Q5: **

A particle started moving in a straight line from point towards point .
Its velocity after seconds is given by
After 2 seconds, another particle started moving in a straight line from point towards point .
This particle was accelerating at 0.9 m/s^{2}.
The two particles collided 6 seconds after the first particle started moving.
Find the distance .

**Q6: **

A particle, starting from rest, began moving in a straight line. Its acceleration , measured in metres per second, and the distance from its starting point, measured in metres, satisfy the following equation . Find the speed of the particle when .

- A
- B
- C
- D

**Q7: **

A body moves in a straight line. At time seconds, its acceleration is given by Given that the initial displacement of the body is 9 m, and when , its velocity is 27 m/s, what is its displacement when ?

**Q8: **

A particle is moving in a straight line such that its velocity after seconds is given by Find the distance covered during the time interval between and .

**Q9: **

A particle is moving in a straight line such that its acceleration, meters per second squared, and displacement, meters, satisfy the equation . Given that the particle's velocity was 12 m/s when its displacement was 0 m, find an expression for in terms of , and determine the speed that the particle approaches as its displacement increases.

- A ,
- B ,
- C ,
- D ,

**Q10: **

A particle is moving in a straight line such that its velocity at time seconds is given by Given that its initial position , find an expression for its position at time seconds.

- A m
- B m
- C m
- D m

**Q11: **

The figure shows a velocity-time graph for a particle moving in a straight line. Find the magnitude of the displacement of the particle.

**Q12: **

The diagram below shows the acceleration of a particle which was initially at rest. What was its velocity at ?

**Q13: **

A particle started moving in a straight line. Its acceleration at time seconds is given by Find the maximum velocity of the particle and the distance it travelled before it attained this velocity.

- A ,
- B ,
- C ,
- D ,

**Q14: **

A particle moves in a straight line. At time seconds, its velocity, in meters per second, is given by What is its displacement in the interval ?

**Q15: **

A particle started moving in a straight line such that its acceleration, measured in meters per second, and its displacement from a fixed point, measured in meters, satisfy the following equation: . Given that its initial displacement from the fixed point was 9 meters and its initial velocity was 5 m/s, determine its velocity when .

- A 22 m/s
- B 9 m/s
- C 21 m/s
- D 4 m/s

**Q16: **

A particle moves along the axis. It is initially at rest at the origin. At time seconds, the particleβs acceleration is given by How long does it take for the particle to return to the origin?

- A s
- B s
- C s
- D s
- EThe particle will never return to the origin.

**Q17: **

A particle is moving in a straight line such that its acceleration at time seconds is given by Given that its initial velocity is m/s and its initial position from a fixed point is m, determine its position when seconds.

- A m
- B m
- C m
- D m

**Q18: **

A particle started moving from rest along the -axis from a point at . Its acceleration at time seconds is given by Express its velocity and its displacement after time seconds.

- A ,
- B ,
- C ,
- D ,

**Q19: **

A particle started moving from a fixed point in a straight line such that its acceleration , measured in metres per second squared, and its position , measured in metres, satisfy the following equation: . Given that the initial velocity of the particle was 2 m/s, find an expression for in terms of .

- A
- B
- C
- D

**Q20: **

A particle starts from rest and moves in a straight line. At time seconds, its velocity is given by How long does it take for the particle to return to its starting point?

**Q21: **

The acceleration-time graph of a particle which was initially at rest is shown below. What was its velocity at ?

**Q22: **

A particle is moving in a straight line such that its velocity at time seconds is given by Given that when seconds its position from a fixed point is , find an expression for in terms of .

- A
- B
- C
- D

**Q23: **

The given acceleration-time graph represents the motion of a particle. Given that the particle moved in a straight line and was at rest at time , find the velocity of the particle at .

**Q24: **

A particle started moving on the -axis from the origin at an initial velocity . At time seconds, the particleβs acceleration is given by Given that after 6 seconds, the particleβs displacement was 75 m in the right from point , Determine . If the body passed by once again, determine its velocity at this moment.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q25: **

Two bodies, initially at rest at the same point, start to move in the same direction along the same straight line. At time seconds , their velocities are given by and . Determine the time taken for the two bodies to be 2β744 cm apart.