Which of the following statements are true at some time during the course of the motion? Check all that apply. Check all that apply. The object can have zero acceleration and, simultaneously, nonzero velocity. The object can have zero velocity and, simultaneously, nonzero acceleration. The object can have zero velocity and, simultaneously, zero acceleration. The object can have nonzero velocity and nonzero acceleration simultaneously.

Complete Question:

An object oscillates back and forth on the end of a spring.

Which of the following statements are true at some time during the course of the motion? Check all that apply. Check all that apply. The object can have zero acceleration and, simultaneously, nonzero velocity. The object can have zero velocity and, simultaneously, nonzero acceleration. The object can have zero velocity and, simultaneously, zero acceleration. The object can have nonzero velocity and nonzero acceleration simultaneously.

a) the object can have zero acceleration and, simultaneously, nonzero velocity

b) the object can have zero velocity and, simultaneously, nonzero acceleration

d) the object can have nonzero velocity and nonzero acceleration simultaneously

Explanation:

For an object oscillating back and forth on the end of a spring, when the object swings to the extremes, it momentarily stops and the velocity becomes zero. Rather than being zero, acceleration is maximum at these points because the net force at these extremes is maximum. This justifies option B

At the middle, which is the equilibrium position, the net force is zero because the object is motionless, and hence the acceleration is zero. At this point, the velocity is maximum and not zero. This justifies option A

When the object is swinging and it is neither at the middle nor at the extremes, both acceleration and velocity are not zero. This justifies option D

It is not possible for both the acceleration and the velocity of the swinging object to be simultaneously zero. Option C is wrong