M2 January 2009 Q1

EdexcelOld spec5 marksPower

1. A car of mass 1500 kg is moving up a straight road, which is inclined at an angle \(\theta\) to the horizontal, where \(\sin\theta = \dfrac{1}{14}\). The resistance to the motion of the car from non-gravitational forces is constant and is modelled as a single constant force of magnitude 650 N. The car’s engine is working at a rate of 30 kW.

Find the acceleration of the car at the instant when its speed is 15 m s\(^{-1}\). (5)

Force diagram: T up the slope, 650 down the slope, R normal, 1500g vertically down — Mark scheme

Scheme	Marks
F = ma parallel to the slope, \(T - 1500g\sin\theta - 650 = 1500a\)	M1* A1
Tractive force, \(30000 = T \times 15\)	M1*
\(a = \dfrac{\frac{30000}{15} - 1500(9.8)\left(\frac{1}{14}\right) - 650}{1500}\)	d*M1
\(0.2\) (m s\(^{-2}\))	A1
	(5)
	(5 marks)