Question

How many times more energy is required to increase the speed of a 2200 pound car by 10 mph if car initially is going 30 mph versus it initially going 80 mph? (convert to metric)

Answer 1

here,

the mass of car , m = 2200 pounds = 997.9 kg

when

initial velocity , u1 = 30 mph = 13.4 m/s

final velocity , v1 = 40 mph = 17.88 m/s

the change in kinetic energy , KE1 = 0.5 * m * ( v1^2 - u1^2)

KE1 = 0.5 * 997.9 * ( 17.88^2 - 13.4^2) J

KE1 = 6.99 * 10^4 J

when

initial velocity , u2 = 80 mph = 35.76 m/s

final velocity , v2 = 90 mph = 40.23 m/s

the change in kinetic energy , KE2 = 0.5 * m * ( v2^2 - u2^2)

KE2 = 0.5 * 997.9 * ( 40.23^2 - 35.76^2) J

KE2 = 1.7 * 10^5 J

the number of times , N = KE2 /KE1

N = 1.7 * 10^5 J /( 6.99 * 10^4 J)

N = 2.42 times

the energy required is 2.42 times