An object in one-dimensional motion reverses direction when which occurs?

An object in one-dimensional motion reverses direction when which occurs?

• A. a(t) = 0
• B. v(t) = 0
• C. ∫ v(t) dt = 0
• D. v(t) switches signs

Answer: (D)

In one-dimensional motion, the direction of travel is shown by the sign of velocity. Reversing direction means the velocity changes from positive to negative or from negative to positive. So the moment of reversal is exactly when v(t) switches signs. It’s the sign change that tells you the motion has flipped direction, even though the velocity may be zero at that instant in a smooth path. Acceleration being zero doesn’t force a reversal, and having the integral of velocity (the displacement) be zero over an interval doesn’t by itself specify when or if the direction flips.

In one-dimensional motion, the direction of travel is shown by the sign of velocity. Reversing direction means the velocity changes from positive to negative or from negative to positive. So the moment of reversal is exactly when v(t) switches signs. It’s the sign change that tells you the motion has flipped direction, even though the velocity may be zero at that instant in a smooth path. Acceleration being zero doesn’t force a reversal, and having the integral of velocity (the displacement) be zero over an interval doesn’t by itself specify when or if the direction flips.