Question

A car is travelling with linear velocity v on a circular road of radius R. If its speed is increasing at the rate of a $m/s^2$, then the net acceleration will be

• A. $\frac{v^2}{R}+a$
• B. $\frac{v^2}{R}-a$
• C. $\sqrt{{\left(\frac{v^2}{R}\right)}^2+a^2}$
• D. $\sqrt{{\left(\frac{v^2}{R}\right)}^2-a^2}$

Answer 1

Answer: (C)

$\sqrt{{\left(\frac{v^2}{R}\right)}^2+a^2}$

As give the tangential acceleration is $a$

and the centripetal acceleration is $a_c=\frac{v^2}{R}$ which is directed towards the $center$ i.e along $radius$ so it will be

$perpendicular$ to the $tangential$ acceleration, so the net acceleration will be $\sqrt{a_c^2+a^2}=\sqrt{(\frac{v^2}{R}{)}^2+a^2}$