A ball hits a vertical wall horizontally at $10\,m{s^{ - 1}}$ bounces back at $10\,m{s^{ - 1}}$
A. There is no acceleration because $10\,m{s^{ - 1}} - 10\,m{s^{ - 1}} = 0$
B. There may be an acceleration because its initial direction is horizontal
C. There is an acceleration because there is a momentum change
D. Even though there is no change in momentum there is a change in direction. Hence it has an acceleration.

Hint:In order to solve this question, we will use the concept of newton’s second law of motion which says that force on a body is equal to the rate of change in momentum of the body and where there is force there is acceleration, so using this we will determine the correct option.

Formula used:
The expression of linear momentum is,
$P=mv$
Where, $m$ is the mass of a body and $v$ is the velocity.

Complete step by step solution:
According to the question, we have given that before hitting the wall initial velocity of the body is $10\,m{s^{ - 1}}$ so initial momentum of the ball is
$P = mv \\
\Rightarrow P = 10m $
where m is the mass of the ball and after hitting the wall, the ball bounces back at the velocity of $10\,m{s^{ - 1}}$.

So the direction will be opposite of the initial direction so the final momentum of the ball will be,
$P' = mv' \\
\Rightarrow P' = - 10m \\ $
So, the change in momentum of the ball will be,
$\Delta P = P - P' \\
\therefore \Delta P = 20m $
Since there is a definite change in the momentum of the ball, so according to the second law of motion if there is change in momentum of the body, a force must act on it and due to applied force a body must have an acceleration.

Hence, the correct answer is option C.

Note: It should be remembered that force is defined as the product of mass and acceleration of the body so whenever force acts on a body it gets accelerated and due to acceleration the velocity of body changes which result in change in momentum of the body.