Question

A body moves in a circle of radius $1\text{m}$, whose speed varies with time $t$(in $s$) as $v=2t^{2}m{s}^{-1}$. Find the net acceleration at $t=2\text{seconds}$.

• A. $\sqrt{1616}{\text{m/s}}^2$
• B. $\sqrt{3240}{\text{m/s}}^2$
• C. $\sqrt{3814}{\text{m/s}}^2$
• D. $\sqrt{4160}{\text{m/s}}^2$

Answer 1

The correct option is D $\sqrt{4160}{\text{m/s}}^2$

Let the tangential acceleration be $a_t$
$a_t=\frac{dv}{dt}=4t$
$\therefore a_t{|}_{t=2}=4\left(2\right)=8{\text{m/s}}^2$

Let the centripetal acceleration be $a_c$
$a_c=\frac{v^2}{R}$
$\Rightarrow {\begin{array}{c}{a}_c\end{array}|}_{t=2\text{sec}}=\frac{{\left[2\right(2{)}^2]}^2}{1}=8^2{\text{m/s}}^2=64{\text{m/s}}^2$

Net acceleration
$\therefore a_{\text{net}}=\sqrt{a_c^2+a_t^2}=\sqrt{{64}^2+8^2}$
$=\sqrt{4160}{\text{m/s}}^2$