In one-dimensional motion, if an object's velocity remains constant in time, what is its acceleration?

• A. Constant and nonzero
• B. Increasing linearly with time
• C. Undefined because velocity is constant
• D. $0$

Answer: (D)

Verified step by step guidance

1. Recall the definition of acceleration as the rate of change of velocity with respect to time, which can be written as \(a = \frac{dv}{dt}\).
2. Since the problem states that the object's velocity remains constant in time, this means \(v\) does not change as time progresses.
3. If velocity is constant, then the change in velocity \(\Delta v\) over any time interval \(\Delta t\) is zero, so \(\frac{\Delta v}{\Delta t} = 0\).
4. Taking the limit as \(\Delta t\) approaches zero, the instantaneous acceleration \(a = \frac{dv}{dt} = 0\).
5. Therefore, when velocity is constant, the acceleration must be zero.