Question

The velocity of a particle is zero at time $t=2 \, s$ , then

• A. displacement must be zero in the interval $t=0$ to $t=2s.$
• B. acceleration may be zero at $t=2s.$
• C. velocity must be zero for $t>2s.$
• D. acceleration must be zero at $t=2s.$

Answer 1

Answer: (B)

Let us consider an example in which particle is projected vertically upwards from ground at $t=0$ and it reaches the highest point at $t=2 \, s$ .
Then, at that instant $\left(\right.t=2 \, s\left.\right)$ velocity $v=0$ , but acceleration $=-g$ .
Here, displacement is non zero for the duration $t=0 \, to \, t=2 \, s$ . For $t>2 \, s$ the ball again acquires velocity. In this example option $\left(\right.1\left.\right), \, \left(\right.3\left.\right)$ and $\left(\right.4\left.\right)$ are incorrect.
Let us consider another example in which a particle is moving on a horizontal plane and it comes to rest permanently at $t=1 \, s$ , then this is one of the special case in which acceleration of the particle is zero at $t=2 \, s$ .