Question

The speed of a particle moving in a circle of radius $r=2m$ 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 $t=2s$ .

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

Answer 1

Answer: (A)

The linear speed of the particle at $t=2s$ is
$v=2^2=4$ $m{s}^{-1}$
$\therefore$ Radial acceleration $a_r=\frac{v^2}{r}=\frac{{\left(4\right)}^2}{2}=8m{s}^{-2}$
The tangential acceleration is $a_t=\frac{dv}{dt}=2t$
$\therefore$ Tangential acceleration at $t=2s$ is
$a_t=\left(2\right)\left(2\right)=4m{s}^{-2}$
$\therefore$ 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 $a=\sqrt{80}m{s}^{-2}$