Question

Can a body have zero velocity and still be accelerating?

Answer 1

Hint : Velocity of a body is the rate of change of displacement and the acceleration of a body is the rate of change of velocity. Both are vector quantities so have both magnitude and direction.

Formula Used: The formulae used in the solution are given here,
 $\Rightarrow a = \dfrac{{\vartriangle v}}{{\vartriangle t}} = \dfrac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}} $ where $ \vartriangle v $ is the change in velocity and $ \vartriangle t $ is the change in time.

Complete step by step answer
Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity as it has both magnitude and direction. Let acceleration of a body be equal to $ a $ .
$\Rightarrow a = \dfrac{{\vartriangle v}}{{\vartriangle t}} = \dfrac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}} $ where $ \vartriangle v $ is the change in velocity and $ \vartriangle t $ is the change in time. Let us assume the final velocity of a body is $ {v_2} $ and the initial velocity of the body is $ {v_1} $ , the $ {t_2} - {t_1} $ represents the duration of change in velocity.
Let us consider a few examples.
An object is thrown straight up. The body undergoes uniformly accelerated motion, where the acceleration is equal to the acceleration due to gravity even when the body reaches its maximum height where it stops, its velocity is zero.
Again, when a ping-pong ball is thrown to the ground, it rises shortly after it hits the ground. Its direction of motion has changed, thus decreasing its velocity to zero. If the acceleration was zero at that point, the ball would fall to the ground and stick to it. This doesn’t happen. The ball rises from the ground instead, implying that the acceleration increases to the point when it is greater than acceleration due to gravity.
Another example would be to look at an object in a vehicle that stops at the traffic signal. Once the signal turns green, the vehicle is accelerated to attain a velocity so that the vehicle moves. In this whole scenario, when the vehicle starts from rest there must be a point of time when the velocity is zero and the acceleration is non zero.
Looking at all the three examples, we can conclude that a body can have zero velocity and non-zero acceleration.

Note
There can be several other examples to be considered, such a weight attached to a spring which has acceleration due to gravity, but velocity is zero when it is at its maximum stretch. Another example is that of a pendulum that is accelerating even at its extreme points, when the velocity is zero.