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

The correct option is C $\sqrt{{\left(\frac{v^2}{R}\right)}^2+a^2}$

R.E.F image

$a_c$ = centripetal acceleration = $\frac{v^2}{R}$

$a_t$= tangential acceleration =a

$a_{net}$ =$\sqrt{a_c+a+2}$

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

option (C)