Question

A racing car is moving around the circular track of radius 300 meters shown above. at the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second squared. when viewed from above, the car is moving clockwise at 30 m/s clockwise at 10 m/s counterclockwise at 30 m/s counterclockwise at 10 m/s

Answer 1

Answer:

the car is moving clockwise at 30 m/s

Explanation:

For an object moving in circular motion:

- The velocity is always tangential to the circle

- The acceleration (centripetal acceleration) is towards the centre of the circle, so perpendicular to the velocity)

In this case, the velocity is directed due east, while the acceleration is directed due south: so the car is "curved towards south while moving", this means that the car is travelling clockwise.

Moreover, the centripetal acceleration is given by:

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

where

a = 3 m/s^2 is the acceleration

v is the speed

r = 300 m is the radius of the track

Solving for v,

$v=\sqrt{ar}=\sqrt{(3 m/s^2)(300 m)}=30 m/s$

So the answer is

the car is moving clockwise at 30 m/s