A car travels the same distance at constant speed around two curves, one with twice the radius of curvature of the other. For which of these curves is the change in velocity of the car greater? Explain.

The answer is below

Explanation:

Centripetal acceleration is the acceleration due to the movement of an object in a uniform circular motion. The acceleration is directed towards the center of the circle.

Centripetal acceleration is given by the formula:

a = v² / r; where v is the speed of the object and r is the radius of curvature (distance from object ot the center of circle).

Let us assume the car has a velocity of v m/s. For the curve with radius of curvature r:

a₁ = v² / r

For the curve with radius of curvature r = 2r:

a₂ = v² / 2r = (1/2)a₁

Therefore the centripetal acceleration is greater in the curve with radius pf curvature r and smaller in the curve with twice the radius of curvature of the other.