Question
If velocity is constant, then acceleration is what? Choose one:
- (a) zero
- (b) constant, but not necessarily zero
- (c) constant
- (d) not need more information
Answer
Choose (a) zero.
Acceleration is the time derivative of the velocity vector:
If is constant, neither its magnitude nor its direction changes, so . Therefore the acceleration is zero. Option (b) is false because a nonzero constant acceleration would make velocity change with time. Option (c) is too broad: zero is the specific constant value. Option (d) is unnecessary because the stated condition already determines the result.
Constant speed alone would not be enough. In uniform circular motion, speed is constant while the velocity direction changes, producing centripetal acceleration. The question says constant velocity, not merely constant speed.
Evidence boundary
The answer treats velocity as a vector measured in one inertial reference frame and constant throughout the interval in question. It does not claim that every motion with constant speed has zero acceleration; a changing velocity direction can produce nonzero acceleration even when speed stays fixed.
Sources
These references support the concepts and methods used in the explanation above.