Question

The speed of a particle moving in a circle of radius $r=2 \, m$ varies with time $t$ as $v=t^{2}$ where t is in second and $v$ is in $m \, s^{- 1}$ . Find the net acceleration at $t=2 \, s$ .

• A. $\sqrt{80} \, m \, s^{- 2}$
• B. $\sqrt{90}ms^{- 2}$
• C. $\sqrt{120}ms^{- 2}$
• D. $\sqrt{70}ms^{- 2}$

Answer 1

Answer: (A)

The linear speed of the particle at $t=2s$ is
$v=2^{2}=4$ $ms^{- 1}$
$\therefore $ Radial acceleration $a_{r}=\frac{v^{2}}{r}=\frac{\left(4\right)^{2}}{2}=8ms^{- 2}$
The tangential acceleration is $a_{t}=\frac{d v}{d t}=2t$
$\therefore $ Tangential acceleration at $t=2s$ is
$a_{t}=\left(2\right)\left(2\right)=4ms^{- 2}$
$\therefore $ Net acceleration of at $t=2s$ is
$a=\sqrt{\left(a_{r}\right)^{2} + \left(a_{t}\right)^{2}}=\sqrt{\left(8\right)^{2} + \left(4\right)^{2}}$
Or $a=\sqrt{80}ms^{- 2}$