Question

A radius vector of a particle varies with time $t$ as $r=at(1-\alpha t)$, where $a$ is a constant vector and $\alpha$ is a positive constant.

Find the the acceleration $w$ of the particle as functions of time.

• A. $w=-4\alpha a$
• B. $w=2\alpha a$
• C. $w=4\alpha a$
• D. $w=-2\alpha a$

Answer 1

The correct option is D $w=-2\alpha a$

$v=\frac{dr}{dt}$
$v=a-2a\alpha t$
$\omega =\frac{dv}{dt}$
$\omega =-2a\alpha$
Hence answer is D.