Question

A body moves in a circle of radius $1\text{m}$. Its speed is given by $v=2t^2$. Find the net acceleration at $t=2\text{s}$

• 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 $a_t$
and centripetal acceleration be $a_c$

Its speed is given by $v=2t^2$

$a_t=\frac{dv}{dt}=4t$
$\therefore$ at $t=2s$,
$a_t=4\left(2\right)=8{\text{m/s}}^2$

Now for the centripetal acceleration,
$a_c=\frac{v^2}{R}$
At $t=2s,v=2\times 2^2=8m/s$
$\Rightarrow a_c=\frac{8^2}{1}=64{\text{m/s}}^2$

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

Hence option D is the correct answer.