A toy racing car moves with constant speed around the circle shown below. When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s). When it is at point B its velocity and acceleration are: A) −(6 m/s) and (12 m/s²), respectively B) (6 m/s) and −(12 m/s²), respectively C) (6 m/s) and (12 m/s²), respectively D) (6 m/s) and (10 m/s²), respectively E) (6 m/s) and 0 m/s², respectively

Question

Quizplus · Accepted Answer

Since the car is moving at constant speed, its velocity at all points on the circle must be the same magnitude (6 m/s). At point B, the velocity vector is tangent to the circle and pointing to the right as the car is moving clockwise around the circle. Therefore, the velocity vector is (6 m/s) to the right.
Since the car is accelerating, there must be a force acting on it that is causing the change in its motion. This force must be directed towards the center of the circle (since the car is moving in a circle) and have a magnitude equal to the centripetal force required to keep the car moving in a circle at that speed. The magnitude of the centripetal force is given by Fc = mv2/r, where m is the mass of the car, v is its speed, and r is the radius of the circle. The acceleration vector is then given by a = Fc/m, where m is the mass of the car. The centripetal force is directed towards the center of the circle and the acceleration vector is in the same direction as the centripetal force.
Since the velocity vector is pointing to the right at point B and the acceleration vector is directed towards the center of the circle, the acceleration vector must be pointing downwards (i.e. towards the bottom of the page). The magnitude of the acceleration is given by a = Fc/m = (mv2/r)/m = v2/r = (6 m/s)2/0.5 m = 72 m/s2. Therefore, the acceleration vector has a magnitude of 72 m/s2 directed towards the center of the circle, which is downwards. The direction can also be specified using a negative sign, so the answer is (6 m/s) and (12 m/s2 downwards), which corresponds to choice C.

A Toy Racing Car Moves with Constant Speed Around the Circle