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

Answer:

Factor by which kinetic energy increase = 4 times

Step-by-step explanation:

Given,

• Mass of the car, v1 = 1500 kg

• initial speed of car = 35 miles/h

                               $=\dfrac{35\times 1609.34}{3600}\ m/s$

                               = 15.64 m/s

Initial kinetic energy of the car is given by,

$k_1\ =\ \dfrac{1}{2}.m.v_1^2$

       $=\ \dfrac{1}{2}\times 1500\times (15.64)^2\ joule$

       = 183606.46 J

• Final velocity of car v2 = 70 miles/hour

                                      $=\dfrac{70\times 1609.34}{3600}$

                                      = 31.29 m/s

So, final kinetic energy of car is given by

$k_2\ =\ \dfrac{1}{2}.m.v_2^2$

        $=\ \dfrac{1}{2}\times 1500\times (31.29)^2$

        = 734425.84 J

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

$\dfrac{k_2}{k_1}=\ \dfrac{734425.84}{183606.46}$

$=>\ k_2\ =\ 4k_1$                      

Hence, the kinetic energy will increase by 4 times.