Question

A car is moving in a circular path of radius $500m$ with a speed of $30m/s$. If the speed is increasing at the rate of 2m/s${}^2$, the resultant acceleration will be

• A. $2m/s^2$
• B. $2.5m/s^2$
• C. $2.7m/s^2$
• D. $4m/s^2$

Answer 1

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

$r=500m,v=30m/s,a_T=2m/s^2$
Resultant acceleration,
$a_C=\frac{v^2}{r}=\frac{30\times 30}{500}=\frac{9}{5}=1.8m/s^2$
Resultant acceleration,
$a=\sqrt{a_T^2+a_C^2}=\sqrt{2^2+{1.8}^2}=2.7m/s^2$