Question

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

• A. $\sqrt{\frac{v^2}{r^2}-a^2}$
• B. $\sqrt{\frac{v^4}{r^2}+a^2}$
• C. $\sqrt{\frac{v^4}{r^2}-a^2}$
• D. $\sqrt{\frac{v^2}{r^2}+a^2}$

Answer 1

Answer: (B)

Centripetal acceleration $=\frac{v^2}{r}$ and it is perpendicular to increase in speed a which is tangential

$\therefore$ Resultant acceleration
$=\sqrt{{\left(\frac{v^2}{r}\right)}^2+\left(a^2\right)}$