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 velocity $v$ of the particle as a function of time.

• A. $\overrightarrow{v}=a(1+2\alpha t)$
• B. $\overrightarrow{v}=a(1-2\alpha t)$
• C. $\overrightarrow{v}=a(1+4\alpha t)$
• D. $\overrightarrow{v}=a(1-4\alpha t)$

Answer 1

Answer: (B)

$\overrightarrow{v}=a(1-2\alpha t)$

$r=at(1-\alpha t)\Rightarrow v=\frac{dr}{dt}=a(1-2\alpha t)$