Question

A body moves in a circle of radius $1m$. Its speed is given by $v=2t^2$. FInd the net acceleration at $t=2$ seconds.

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

Answer 1

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

Let the tangential acceleration be $a_t$
and centripetal acceleration be $a_c$
$a_t=\frac{dv}{dt}=4t$
$\therefore a_t{|}_{t=2sec}=4\left(2\right)=8m/s^2$
$a_c=\frac{v^2}{R}$
$\Rightarrow a_c{|}_{t=2sec}=\frac{\left[2\right(2{)}^2{]}^2}{1}=8^{2}m/s^2$
$=64m/s^2$
$\therefore a_{net}=\sqrt{a_c^2+a_t^2}=\sqrt{{64}^2+8^2}$
$=\sqrt{4160}m/s^2$