Acceleration is defined as the change in velocity over time, but there can be situations where acceleration is not equal to the change in velocity over time. Here are a few scenarios:
Changing direction without a change in speed: Acceleration is a vector quantity that takes into account both the magnitude and direction of velocity. If an object changes its direction without a change in speed, there is still a change in velocity, but the magnitude of velocity remains the same. In this case, the acceleration is present due to the change in direction, but the change in velocity over time is zero.
Uniform circular motion: When an object moves in a circular path at a constant speed, its velocity is constantly changing direction, resulting in an acceleration toward the center of the circle. This acceleration is called centripetal acceleration. Although the speed may remain constant, the velocity is changing due to the change in direction, resulting in non-zero acceleration.
Instantaneous changes: Acceleration is defined as the rate of change of velocity over time. If there is an instantaneous change in velocity, such as during a collision or a sudden change in direction, the acceleration at that instant can be very high or infinite. However, over a finite time interval, the change in velocity may not be accurately captured by the average acceleration, as it cannot account for the instantaneous changes.
Variable acceleration: In cases where the acceleration is not constant but varies over time, the change in velocity over a specific time interval may not be accurately represented by the average acceleration. In such situations, the instantaneous acceleration at different points in time needs to be considered to determine the actual change in velocity.
It's important to note that in most common cases of uniform acceleration or constant acceleration, the acceleration is indeed equal to the change in velocity over time. The examples mentioned above highlight specific scenarios where acceleration may not be directly proportional to the change in velocity over time.