Question

A motor car is traveling at 30 $m{s}^{-1}$ on a circular road of radius $500$ m. It is increasing speed at the rate of $2$ $m{s}^{-2}$. The acceleration of car is :

• A. 2 $m{s}^{-2}$
• B. 2.7 $m{s}^{-2}$
• C. 3 $m{s}^{-2}$
• D. 3.7 $m{s}^{-2}$

Answer 1

The correct option is B 2.7 $m{s}^{-2}$

Given $a_T=2m{s}^{-2}$
and $a_r=\frac{v^2}{r}=\frac{30\times 30}{500}=1.8m{s}^{-2}$
$\therefore a=\sqrt{a_r^2+a_t^2}=\sqrt{{1.8}^2+2^2}$
$=2.7m{s}^{-2}$