Question

A car has mass 1500 kg and is traveling at a speed of 35 miles/hour. what is its kinetic energy in joules? (Be sure to convert miles/hour to m/s). If the car increases its speed to 70 miles/hour, by what factor does its kinetic energy increase? show work

Answer 1

Factor by which kinetic energy increase = 4 times

Explanation:

Given,

• Mass of the car, v1 = 1500 kg

• initial speed of car = 35 miles/h

`=(35* 1609.34)/(3600)\ m/s`

= 15.64 m/s

Initial kinetic energy of the car is given by,

`k_1\ =\ (1)/(2).m.v_1^2`

`=\ (1)/(2)* 1500* (15.64)^2\ joule`

= 183606.46 J

• Final velocity of car v2 = 70 miles/hour

`=(70* 1609.34)/(3600)`

= 31.29 m/s

So, final kinetic energy of car is given by

`k_2\ =\ (1)/(2).m.v_2^2`

`=\ (1)/(2)* 1500* (31.29)^2`

= 734425.84 J

Now, the ratio of final to initial kinetic energy can be given by,

`(k_2)/(k_1)=\ (734425.84)/(183606.46)`

`=>\ k_2\ =\ 4k_1`

Hence, the kinetic energy will increase by 4 times.