Question

The displacement of a particle varies with time $t$ as: $s=\alpha t-\beta t^2$. Determine the time $\left(t\right)$ at which velocity of the particle becomes $0$.

• A. $\frac{\alpha }{2\beta }$
• B. $\frac{\alpha }{\beta }$
• C. $\frac{2\alpha }{\beta }$
• D. $\frac{\alpha }{4\beta }$

Answer 1

The correct option is A $\frac{\alpha }{2\beta }$

Given,
$s=\alpha t-\beta t^2$
Differentiating $s$ w.r.t $t$ we get,
$v=\frac{ds}{dt}=\alpha -2\beta t$

As $v=0$, we get $\alpha -2\beta t=0\Rightarrow t=\frac{\alpha }{2\beta }$