Answer to Question #124467 in Classical Mechanics for rishabh

Question

a car going around a circular racetrack of radius 100m at 20 m/s2 experiences an acceleration of 4m/s2. what would be the acceleration if the radius of the track was increased to 200m?

Answer 1

Given, tangential velocity is $v=20m/s$ .

Now, if radius was actually $r=200m$ and Tangential acceleration is $a_t=4m/s^2$

Now, radial acceleration will be,

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

Thus, $a_r=2m/s^2$ .

Therefore, acceleration of the car will be

$$a=\sqrt{a_t^2+a_r^2}=2\sqrt{5}m/s^2$$