A car runs out of fuel at the top of hill $A.$ The driver hopes to get to the service station by letting the car roll downhill with its engine switched off. There is a small hill, B$,$ in between as shown. The distance from hill A to hill B along the road is $0\mathrm{.}2km$ and from hill $B$ to the service station is $0\mathrm{.}4km.$

The top of hill A is $50\mathrm{.}0m$ above the service station and the top service station.

$($a$)$ When the car reaches hill $B$ its speed is $5\mathrm{.}0m{s}^{-1}.$ Assuming that the car starts from rest at hill A$,$ show that the average frictional force acting on the car is $750N.$ The mass of the car is $800kg.$

$[5]$

$($b$)$ Assuming that the frictional force remains constant throughout, determine whether or not the car reaches the service station.

$[3]$

$S+SN$ and the $P_{}$ is a reator

$($c$)$ Besides friction in the wheels and tyres, name andther source of frictional resistance for the moving car, and explain why it will not in fact remain constant during the motion.

$[2]$

Ais resutance.