Question

A sports car traveling along a straight line increases its speed from 19.8 mi/h to 59.9 mi/h.a. What is the ratio of the final to theinitial magnitude of its momentum?b. What is the ratio of the final to the initial kineticenergy?

Answer 1

Answer

given,

initial speed of the car (v₁)= 19.8 mi/h

final speed of the car (v₂)= 59.9 mi/h

a) initial momentum = m v₁

                   P₁ = 19.8 m

  final final momentum = m v₂

                   P₂ = 59.9 m

      ratio = $\dfrac{P_2}{P_1}$

              =$\dfrac{59.9 m}{19.8 m}$

      ratio of momentum=$\dfrac{P_2}{P_1}=3.025$

b) initial kinetic energy= 1/2 m v₁²

                   K₁ = 196.02 m

  final kinetic energy= 1/2 m v₂²

                   K₂ = 1794.005 m

      ratio = $\dfrac{K_2}{K_1}$

              =$\dfrac{1794.005 m}{196.02 m}$

      ratio of Kinetic energy=$\dfrac{P_2}{P_1}=9.15$