Question

A car moving with speed $30m/s$ on a circular path of radius $500m$. Its speed is increasing at the rate of $2m/se{c}^2$. The magnitude of total acceleration of the car is

• A. $9.8m/se{c}^2$
• B. $1.8m/se{c}^2$
• C. $2m/se{c}^2$
• D. $2.7m/se{c}^2$

Answer 1

The correct option is D $2.7m/se{c}^2$

$\text{Step 1: Tangential acceleration calculation}$

Let $a_t$ be the tangential acceleration.

Rate of increase of speed $=a_t$

$\therefore a_t=2m/s^2$

$\text{Step 2: Centripetal acceleration calculation}$

Centripertal acceleration, $a_c=\frac{v^2}{R}$ $=\frac{(30m/s{)}^2}{500m}$$=1.8m/s^2$

$\text{Step 3: Total acceleration [Refer Fig.]}$

Since tangential and centripetal acceleration are at ${90}^{\circ }$

$\therefore a=\sqrt{a_t^2+a_c^2}$

$=\sqrt{2^2+{1.8}^2}=2.7m/s^2$

Hence option $D$ is correct.