Question

A car is moving on a circular track of radius 100 m with a net acceleration of $7m/s^2$. If the speed of the car is increasing at the rate of $5m/s^2$, its speed is

• A. 15 m/s
• B. 22 m/s
• C. 30 m/s
• D. 10 m/s

Answer 1

The correct option is B 22 m/s

The tangential acceleration is given by $a_t=5m/s^2$ and the net acceleration $a=7m/s^2$.
We know that tangential and radial acceleration are perpendicular to each other.
Thus, $a^2=a_r^2+a_t^2$. Substituting the values of $a_r$ and $a$, we get $a_r=\sqrt{49-25}=2\sqrt{6}=4.89m/s$
The radial acceleration is related to linear velocity as $a_r=v^2/R$. Thus, $v=\sqrt{a_{r}R}=\sqrt{4.89\times 100}=22m/s)$
The correct option is (b)