Kinematics

Understanding the equation of motion.
The position of the particle is
given by:
For the particle to return to its starting position, the displacement must be zero. Thus, we set : Solving for , we get: Thus, the particle returns to its starting position after . Thus, the correct answer is
(B)
.

Step 1: Find the expression for velocity.
Velocity is the first derivative of distance with respect to time :
Step 2: Find the expression for acceleration.
Acceleration is the derivative of velocity with respect to time:
Step 3: Find when acceleration is zero.
Set :
Step 4: Find the velocity when acceleration is zero.
Substitute into the velocity equation:
Conclusion:
The velocity of the particle when its acceleration is zero is .
Conclusion:
The correct answer is (D) -9 m/s.