How is it possible to be accelerating and traveling at a constant speed?

Answer 1

Acceleration is the change in velocity with respect to time. Velocity is the change in position with respect to time (not the change in speed with respect to time, as you have written). Both acceleration and velocity are vector quantities, which means they have both a magnitude and a direction.

Speed is simply the magnitude of the velocity. (It's what's called a "scalar" quantity, which is just a number without an associated direction.) An object can have a constant speed, but its direction of motion can be changing over time, so it's velocity is changing. The resulting nonzero change in velocity per unit time is the acceleration.

An object need not be moving in a circle to meet these conditions. An object that moves at constant speed, but follows any path that is not a straight line must experience an acceleration. A circular path (like a satellite's orbit) is simply one example example of this.

Answer 2

It is possible to be accelerating and traveling at a constant speed if the direction of the acceleration is perpendicular to the direction of motion. For example, if an object is moving in a circular path at a constant speed, it is constantly changing direction, which means it is accelerating towards the center of the circle. This acceleration does not change the speed of the object, but it does change its velocity by constantly changing its direction.

Answer 3

Acceleration refers to any change in velocity, which includes changes in speed, direction, or both. It is possible to be accelerating and still traveling at a constant speed if the acceleration is purely in a change of direction, such as moving in a circle at a constant speed. In this case, the velocity is changing due to the change in direction, even though the speed remains constant.

Answer 4

If you accelerate, your velocity isn't constant.