Question

A car is moving at a speed of $40m/s$ on a circular track of radius $400m$. This speed is increasing at the rate of $3m/s^2$. The acceleration of car is :

Answer 1

Velocity $v=40m/s$

radius $r=400m$

$\frac{dv}{dt}=3m/s^2$

Centripetal acceleration

$a_c=\frac{v^2}{r}=\frac{1600}{400}{a}_c=4m/s^2$

Tangential acceleration $a_t=\frac{dv}{dt}=3m/s^2$

Total acceleration $a=\sqrt{4^2+3^2}=5m/s^2$