The figure represents the velocity of a particle as it travels along the x-axis.At what value (or values)of t is the instantaneous acceleration equal to zero?
A) t = 0
B) t = 0.5 s and t = 2 s
C) t = 1 s

Question

The figure represents the velocity of a particle as it travels along the x-axis.At what value (or values)of t is the instantaneous acceleration equal to zero? 
A) t = 0 
B) t = 0.5 s and t = 2 s 
C) t = 1 s

Quizplus · Accepted Answer

The instantaneous acceleration is given by the derivative of the velocity with respect to time, that is, a = dv/dt. From the graph, we can see that the velocity is increasing from t = 0 to t = 1 s, and decreasing from t = 1 s to t = 2 s. Therefore, the acceleration is positive from t = 0 to t = 1 s and negative from t = 1 s to t = 2 s.

At t = 1 s, the velocity is changing from increasing to decreasing, which means there is a point of transition from positive acceleration to negative acceleration. At this point, the instantaneous acceleration is equal to zero.

Therefore, the correct choice is C) t = 1 s.

The Figure Represents the Velocity of a Particle as It