In one-dimensional motion with constant acceleration, an object’s velocity changes from $v_{\mathrm{i}}$ to $v_{\mathrm{f}}$ over a time interval $\Delta t$. Which expression gives the magnitude of the acceleration?

• A. $\left|\frac{v_{\mathrm{f}}+v_{\mathrm{i}}}{\Delta t}\right|$
• B. $\left|\frac{v_{\mathrm{f}}-v_{\mathrm{i}}}{\Delta t}\right|$
• C. $\left|\frac{\Delta t}{v_{\mathrm{f}}-v_{\mathrm{i}}}\right|$
• D. $\left|v_{\mathrm{f}}-v_{\mathrm{i}}\right|$

Answer: (B)

Verified step by step guidance

1. Recall the definition of acceleration in one-dimensional motion with constant acceleration: acceleration is the rate of change of velocity with respect to time.
2. Express acceleration mathematically as \(a = \frac{v_f - v_i}{\Delta t}\), where \(v_f\) is the final velocity, \(v_i\) is the initial velocity, and \(\Delta t\) is the time interval over which the change occurs.
3. Since the problem asks for the magnitude of the acceleration, take the absolute value of the expression to ensure the result is non-negative: \(|a| = \left| \frac{v_f - v_i}{\Delta t} \right|\).
4. Note that the numerator represents the change in velocity \(\Delta v = v_f - v_i\), so the magnitude of acceleration is the absolute value of the velocity change divided by the time interval.
5. Avoid confusing this with other expressions such as \(\left| \frac{v_f + v_i}{\Delta t} \right|\) or \(\left| \frac{\Delta t}{v_f - v_i} \right|\), which do not represent acceleration.