M2 January 2011 Q1

EdexcelOld spec6 marksPower

1. A cyclist starts from rest and moves along a straight horizontal road. The combined mass of the cyclist and his cycle is 120 kg. The resistance to motion is modelled as a constant force of magnitude 32 N. The rate at which the cyclist works is 384 W. The cyclist accelerates until he reaches a constant speed of \(v\) m s\(^{-1}\).

Find

(a) the value of \(v\), (3)

(b) the acceleration of the cyclist at the instant when the speed is 9 m s\(^{-1}\). (3)

Scheme	Marks
Constant speed \(\Rightarrow\) Driving force \(=\) resistance, \(\ F = 32\).	B1
\(P = F \times v = 32v = 384\)	M1
\(v = 12\ \left(\text{ms}^{-1}\right)\)	A1
	(3)

Scheme	Marks
\(P = F \times v \Rightarrow\ 384 = F \times 9,\ F = \dfrac{384}{9}\)	M1
Their \(\ F - 32 = 120a\),	M1
\(a = 0.089\left(\text{ms}^{-2}\right)\)	A1
	(3)
	(6 marks)