Question

A truck has 5 times the mass of a car and is moving at a speed which is 3 times higher that the speed of the car. By which factor is the kinetic energy of the truck higher than the kinetic energy of the car?

Answer 1

Let mC and vC be the mass and speed of the car and mT and vT be those of the truck. Given,

$m_{T}=5m_{C}$

UT 3uc

The kinetic energy of the car is,

$KE_{C}=\frac{1}{2}m_{C}v{_{C}}^{2}$

The kinetic energy of the truck is,

$KE_{T}=\frac{1}{2}m_{T}v{_{T}}^{2}$

$KE_{T}=\frac{1}{2}(5m_{C})(3v_{C})^{2}=45(\frac{1}{2}m_{C}v{_{C}}^{2})=45KE_{C}$

So the kinetic energy of the truck is 45 times the kinetic energy of the car. Therefore the kinetic energy of the truck is higher than the kinetic energy of the car by a factor of 45.