Question

A car with a mass of 1180 kilograms is being driven at 18.2 meters per second when it runs into a tree. What work is done in pushing in the front of the car? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

According to work energy theorem, the work done in pushing the front of the car is equal to the change in kinetic energy of car.

The change in kinetic energy of the car can be given as,

`\Delta K=(1)/(2)m(v^2-u^2)`

When the car runs into a tree then the final speed of car is 0 m/s.

Substitute the known values in the equation,

`\begin{gathered} \Delta K=(1)/(2)(1180kg)((0m/s)^2-(18.2m/s)^2) \\ =(590kg)(-331.24m^2s^(-2)_{})(\frac{1\text{ J}}{1kgm^2s^(-2)}) \\ =-195431.6\text{ J} \\ \approx-195000\text{ J} \end{gathered}`

According to work energy theorem,

`W=\Delta K`

Substitute the known value,

`W=-195000\text{ J}`

Thus, the work done in pushing the front of car is -195000 J.