When can acceleration be defined as the rate of change of speed?

Acceleration can be defined as the rate of change of speed specifically when an object is moving in a straight line. In this case, speed refers to how fast an object is moving regardless of direction, and acceleration measures how that speed changes over time.

When an object moves in a straight line, any increase or decrease in speed translates directly to acceleration. The formula for acceleration is given by the change in velocity (which is speed with direction) divided by the time taken for that change. Here, because the direction remains constant while speed varies, it simplifies the analysis to just focus on speed as the variable.

In other scenarios, such as moving in circles, the direction of motion changes continuously even if the speed remains constant, which means acceleration is not solely defined by speed but by the change in direction as well. For vertical movements, like moving upward or downward, the concept of speed can still be applied alongside gravity's effects on the object's motion, but understanding acceleration in these cases would generally require considering directional changes alongside speed. Thus, the most straightforward definition of acceleration as the rate of change of speed applies cleanly to straight-line motion.