Question

A car is moving at 55 miles per hour. The kinetic energy of that car is 5 × 105 J.How much energy does the same car have when it moves at 98 miles per hour? Answer in units of J

Answer 1

Given,

Let mass of the vehicle be m

Velocity of the car, v₁ = 55 miles/hr

Since, 1 mile = 1.609 km

=> v₁ = ( (55 * 1.609) * ( 1000 / 3600) ) m/s

           = 24.582 m/s

Kinetic velocity, E₁ = 5 * 10⁵ J

Since,

E = 1/2*m*v²

=> 5 * 10⁵ = 0.5*m*(24.582)² = 0.5 *m*( 604.275 )

=> m = ( 5 * 10⁵ ) / ( 0.5 * 604.275 )

           = 1654.876 kg

Now,

Given

Velocity, v₂ = 98 miles per hor

                    = ( (98 * 1.609) * ( 1000 / 3600 ) ) m/s

                    = 43.801 m/s

Now,

Kinetic energy, E₂ = 1/2*m*v₂² = 0.5 * 1654.876 * ( 43.801 )²

                              = 0.5 * 1654.876 * 1918.527601

                              = 1587462.6411 J

                              = 1.587 * 10⁶ J

or energy is 1.587 * 10⁶ J