Question

A car travelling at $20m/s$ on a circular road of radius $100m$. It is increasing in speed at the rate of $3m/s^2$. Its acceleration is

• A. $3m/s^2$
• B. $4m/s^2$
• C. $5m/s^2$
• D. $7m/s^{-1}$

Answer 1

Answer: (C)

$5m/s^2$

Given : $v=20m/s$ $R=100m$ $\frac{dv}{dt}=3m/s^2$

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

Radial acceleration $a_r=\frac{v^2}{R}=\frac{{20}^2}{100}=4m/s^2$

Total acceleration of the car $a=\sqrt{a_r^2+a_t^2}=\sqrt{4^2+3^2}=5m/s^2$