Question

A motor car is travelling at speed of $30m/s$ on a circular road of radius $500m$. If the speed of the car is increasing at the rate of $2.0m/s^2$, then the total acceleration will be

• A. $1.8m/s^2$
• B. $2m/s^2$
• C. $2.7m/s^2$
• D. $3.8m/s^2$

Answer 1

The correct option is C $2.7m/s^2$

Radial acceleration, $a_r=\frac{v^2}{r}=\frac{{\left(30\right)}^2}{500}=1.8m/s^2$
Tangential acceleration, $a_r=2m/s^2$
$\therefore$ Resultant acceleration, $a=\sqrt{a_r^2+a_r^{2}2a_n{a}_r\cos \theta }$
$\therefore a=\sqrt{{\left(1.8\right)}^2+{\left(2\right)}^2}=\sqrt{7.24}$
$\Rightarrow a=2.7m/s^2$