Question

A car is moving with speed $10m/s$ on a circle path of radius $2m$. If speed is increasing at the rate of $10m/s^2$. The acceleration of car is

• A. $\sqrt{26}m/s^2$
• B. $10\sqrt{26}m/s^2$
• C. $5\sqrt{26}m/s^2$
• D. $10\sqrt{13}m/s^2$

Answer 1

The correct option is B $10\sqrt{26}m/s^2$

Given,

$r=2m$

$v=10m/s$

$a_t=10m/s^2$

Centripetal acceleration,

$a_c=\frac{v^2}{r}$

$a_c=\frac{10\times 10}{2}=50m//s^2$

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

$a=\sqrt{{50}^2+{10}^2}m/s^2$

$a=10\sqrt{26}m/s^2$

The correct option is B.