Question

A motor car is travelling at $30m/s$ on a circular road of radius $500m$. It is increaseing in speed at the rate of $2m/s^2$. Then the acceleration of the car will be

• A. $4m/s^2$
• B. $3m/s^2$
• C. $2.7m/s^2$
• D. $8m/s^2$

Answer 1

The correct option is C $2.7m/s^2$

Given,

$v=30m/s$

$r=500m$

The centripetal acceleration,

$a_c=\frac{v^2}{r}=\frac{30\times 30}{500}=1.8m/s^2$

$a_t=2m/s^2$

The acceleration is given by

$a=\sqrt{(a_t{)}^2+(a_c{)}^2}$

$a=\sqrt{(2{)}^2+(1.8{)}^2}=2.7m/s^2$

The correct option is C.