Physics - Kinematics Question with Solution | TestHub

$\left|\frac{d\vec{v}}{dt}\right|$ is the magnitude of the total acceleration.

$\frac{d|\vec{v}|}{dt}$ is only the rate of change of speed.

They are equal when the direction of $\vec{v}$ is fixed (straight-line motion), so they may be equal. (B) is correct, (A) is wrong.

If $\left|\frac{d\vec{v}}{dt}\right|=0$, then $\vec{v}$ is constant and so is $|\vec{v}|$. (C) is wrong.

If $\frac{d|\vec{v}|}{dt}\ne 0$, the speed itself is changing, so $\left|\frac{d\vec{v}}{dt}\right|\ne 0$. (D) is correct.