Question

An object moves with constant acceleration. Which of the following expression is also constant.

• A. $\frac{d\left|\overrightarrow{v}\right|}{dt}$
• B. $\left|\frac{d\overrightarrow{v}}{dt}\right|$
• C. $\frac{d\left(v^2\right)}{dt}$
• D. $\frac{d\left(\frac{\overrightarrow{v}}{\left|\overrightarrow{v}\right|}\right)}{dt}$

Answer 1

The correct option is B $\left|\frac{d\overrightarrow{v}}{dt}\right|$

Acceleration is constant , thus $\frac{d\overrightarrow{v}}{dt}$ is constant, and thus so will be its magnitude or $|\frac{d\overrightarrow{v}}{dt}$|
Magnitude of velocity may not necessarily be constant. Thus A is incorrect and so is C. D term states that direction or unit vector in direction of acceleration is constant which again need not be the case as acceleration vector means both direction and magnitude.