Question

A car is moving with speed $30m/sec$ on a circular path of radius $500m$. Its speed is increasing at the rate of $2m/{sec}^2$. What is the acceleration of the car at that moment?

Answer 1

Given tangential acceleration, $a_t=2m/s^2$, Tangential speed , $v=30m/s$ and radius , $R=500m$

$\Rightarrow$ centripetal acceleration , $a_c=\frac{v^2}{R}=\frac{{30}^2}{500}=\frac{9}{5}$

Net acceleration is $a=\sqrt{a_t^2+a_c^2}=\sqrt{2^2+{\left(\frac{9}{5}\right)}^2}=\frac{\sqrt{181}}{5}m/s^2$