Question

Consider the image above. Vi = the initial velocity and Vf = the final velocity. Is there acceleration? Explain your answer.
A) No. The initial and final velocities are the same.
B) Yes. The ball had to slow down in order to change direction.
C) No. Acceleration is the change in velocity. The ball's velocity is constant.
D) Yes. Even though the initial and final velocities are the same, there is a change in direction for the ball.

Answer 1

Velocity is a vector, and the initial and final ones are in opposite directions.
There must have been acceleration in order to change the direction of motion.

A) No. The initial and final velocities are the same.
This is all wrong, and not the correct choice.
It's "Yes", and the initial and final velocities are NOT the same.

B) Yes. The ball had to slow down in order to change direction.
This is poor, and not the correct choice.
The "Yes" is correct, but the explanation is bad.
Acceleration does NOT require any change in speed.

C) No. Acceleration is the change in velocity. The ball's velocity is constant.
This is all wrong, and not the correct choice.
It's "Yes", there IS acceleration, and the ball's velocity is NOT constant.

D) Yes. Even though the initial and final velocities are the same, there is a change in direction for the ball.
This choice is misleading too.
The "Yes" is correct ... there IS acceleration.
The change in direction is the reason.
The initial and final velocities are NOT the same.  Only the speeds are.

Answer 2

According to the statements, the answer to the question is yes. Even though the initial and final velocities are the same, there is a change in direction for the ball (option D).

Acceleration is the change in velocity, which is a vector, according to the following equation:

$a = \frac{\Delta v}{\Delta t} = \frac{v_{f} - v_{i}}{t_{f} - t_{i}}$

Where:

$v_{f}$ and $v_{i}$ is the final and initial velocity, respectively

$t_{f}$ and $t_{i}$ is the final and initial time, respectively

         

In the given image, we can see that the magnitude of the final and initial velocity is the same and that directions are opposites, so the acceleration would be:

$a =\frac{v_{f} - v_{i}}{\Delta t} = \frac{(-5 - 5) m/s}{\Delta t} = \frac{-10 m/s}{\Delta t}$      

With this, we can rule out the options:

A. Although the initial and final velocities are the same, the directions are not.

B. The ball does not need to slow down to change direction.  

C. The ball's velocity is not constant (the directions are different).

Therefore, the answer is option D.

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I hope it helps you!