When can an object change its acceleration and not change its speed?
Acceleration is the rate of change of velocity. Velocity is a vector quantity. That means it has magnitude and and direction. Speed is a scalar quantity, it only has magnitude. For example, 10 mph is speed, but 10 mph in a North-East is velocity. So velocity can change when its magnitude changes or there is a change of direction. For example, a car travels 40 mph North-East and then 40 mph West. Same speed but a change of direction means the car has changed its velocity, and since acceleration is rate of change of velocity the a car has accelerated. In this example the acceleration is instantaneous. If the car was going round a curve, then it would be constantly changing direction and hence accelerating. In short to your question, when the object changes direction.
