Question

A sports car moves around a sharp curve with small radius at a speed of 50 mph. A four door family car moves around a wider curve with larger radius at the same speed. The cars have equal mass. Which car changes its direction more quickly ?

Answer 1

The sports car changes its direction more quickly because it moves around a sharper curve with a smaller radius.

Step-by-step explanation:

Centripetal acceleration is proportional to the speed squared and inversely proportional to the radius of the curve. The sports car moves around a sharp curve with a small radius at 50 mph, while the family car moves around a wider curve with a larger radius at the same speed. Since the sports car is moving around a sharper curve, it experiences a higher centripetal acceleration and therefore changes direction more quickly than the family car. Centripetal acceleration is a measure of how quickly an object's direction changes and is given by the formula ac = v^2/r, where v is velocity and r is the radius of the curve. Since both cars have equal mass and speed, the car experiencing the sharper turn will have a higher centripetal acceleration and thus change direction more quickly.