Question

# Can a body have acceleration without having velocity?

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Hint: Choose a few cases where the body is moving in a certain direction, comes to rest and again travels in the same but opposite direction. Now calculate required terms velocity and acceleration at these stages.

Let us take a car moving in a certain direction with some initial velocity $u$and deceleration $a$. After some time, the car eventually comes to rest, i.e, the final velocity is zero. Let’s find out the acceleration at this point where the velocity is zero,
\begin{align} & {{v}^{2}}-{{u}^{2}}=2as \\ & {{(0)}^{2}}-{{u}^{2}}=2(-a)s \\ & a=\dfrac{{{u}^{2}}}{2s} \\ \end{align}
Clearly, at this point, velocity is zero but the object is having some acceleration.
Let us take another example, an object is thrown upward with some initial velocity $u$, when the object reaches the maximum height, the velocity of the object will of course become zero but the acceleration on the object is the gravitational acceleration.
\begin{align} & a=g \\ & g=9.8m{{s}^{-2}} \\ \end{align}
In the above two cases, we’ve seen the cases where an object can have acceleration without any velocity.

If we consider any object that comes to rest in between its journey and again starts moving, we can say that at the point of halt, that object will have zero velocity, as it is at rest for a specific time, but some finite acceleration because it will move again. This kind of situation can be seen when the object is decelerating gradually.
The acceleration will not be zero but the velocity, at some points will become zero.

Note: Acceleration is the change of velocity per unit time. If an object is moving with constant velocity, always keep in mind that the acceleration of the object will be zero as there’s no change in its velocity over a period of time.