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

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 =
`(P_2)/(P_1)`

=
`(59.9 m)/(19.8 m)`

ratio of momentum=
`(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 =
`(K_2)/(K_1)`

=
`(1794.005 m)/(196.02 m)`

ratio of Kinetic energy=
`(P_2)/(P_1)=9.15`