Question

a car of mass 1000 kg rests on a horizontal road initially. it is then pushed over a distance of 5 m to a speed of 1 m/s before the engine is started. if the average frictional force acting on the car is 500 N, the total work done in moving the car before the driver starts the engine?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{The}\mathrm{car}\mathrm{is}\mathrm{pushed}\mathrm{from}\mathrm{rest}\mathrm{to}\mathrm{a}\mathrm{speed}\mathrm{of}1\mathrm{m}/\mathrm{s}\mathrm{over}\mathrm{a}\mathrm{distance}\mathrm{of}5\mathrm{m}. \\ \mathrm{So}\mathrm{the}\mathrm{car}\mathrm{is}\mathrm{accelerated}\mathrm{during}\mathrm{this}\mathrm{push}. \\ \mathrm{Kinetic}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{car}\mathrm{gained}\mathrm{due}\mathrm{to}\mathrm{pushing},\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2 \\ \mathrm{KE}=\frac{1}{2}\times 1000\times {\left(1\right)}^2=500\mathrm{J} \\ \mathrm{Work}\mathrm{done}\mathrm{against}\mathrm{the}\mathrm{friction},\mathrm{W}=\mathrm{frictional}\mathrm{force}\times \mathrm{displacement} \\ \mathrm{W}=500\times 5=2500\mathrm{J} \\ \mathrm{Total}\mathrm{work}\mathrm{done}\mathrm{in}\mathrm{moving}\mathrm{the}\mathrm{car}\mathrm{from}\mathrm{rest}\mathrm{to}\mathrm{a}\mathrm{speed}\mathrm{of}1\mathrm{m}/\mathrm{s}, \\ {\mathrm{W}}_{\mathrm{T}}=2500+500=3000\mathrm{J} \end{gathered}$$