Question

A car is moving with a speed of 30 $m{s}^{-1}$ on a circular path of radius $500m$. Its speed is increasing at the rate of 2 $m{s}^{-2}$. The acceleration of the car at that moment is :

• A. 2.7 $m{s}^{-2}$
• B. 9.8 $m{s}^{-2}$
• C. 2 $m{s}^{-2}$
• D. 1.8 $m{s}^{-2}$

Answer 1

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

$a_t=2m{s}^{-2}$ and $a_c=\frac{v^2}{r}=\frac{(30{)}^2}{500}=\frac{9}{5}m{s}^{-2}=1.8m{s}^{-2}$

net acceleration $a=\sqrt{(a_t{)}^2+(a_c{)}^2}=\sqrt{(2{)}^2+(1.8{)}^2}=\sqrt{7.24}=2.69m{s}^{-2}\approx 2.7m{s}^{-2}$