The equations you mentioned, velocity = displacement/time and speed = distance/time, are not accurate representations of acceleration. Let's clarify the concepts involved:
Velocity: Velocity is a vector quantity that represents both the speed and direction of an object's motion. It is calculated by dividing the displacement (change in position) by the time taken. The formula for average velocity is given by: velocity = displacement / time
Speed: Speed is a scalar quantity that represents only the magnitude of an object's motion, without considering its direction. It is calculated by dividing the distance traveled by the time taken. The formula for average speed is given by: speed = distance / time
Acceleration: Acceleration, on the other hand, is a measure of how an object's velocity changes over time. It is defined as the rate of change of velocity. Mathematically, average acceleration is calculated by dividing the change in velocity by the time taken. The formula for average acceleration is given by: acceleration = change in velocity / time
In the case of constant acceleration, where the rate of change of velocity remains constant, the average acceleration can be represented by the ratio of the change in speed to the time taken, as the direction remains the same. However, it is important to note that acceleration involves the change in velocity, not just speed.
To summarize, while velocity and speed are related to displacement and distance respectively, acceleration is related to the change in velocity over time. Acceleration is not directly equal to velocity/time or speed/time, but rather represents how velocity changes over time.