M1 January 2011 Q5

EdexcelOld spec10 marksTime-Series Graphs

5. A car accelerates uniformly from rest for 20 seconds. It moves at constant speed \(v\) m s\(^{-1}\) for the next 40 seconds and then decelerates uniformly for 10 seconds until it comes to rest.

(a) For the motion of the car, sketch

(i) a speed-time graph,

(ii) an acceleration-time graph.

(6)

Given that the total distance moved by the car is 880 m,

(b) find the value of \(v\). (4)

Speed-time graph: rising from O to v at t = 20, constant to t = 60, falling to zero at t = 70 — Mark scheme (a)

Acceleration-time graph: positive constant, then zero, then negative constant — Mark scheme (a)

Scheme	Marks
1^st section correct	B1
2^nd & 3^rd sections correct	B1
Numbers and \(v\) marked correctly on the axes.	DB1

Scheme	Marks
1^st section correct	B1
2^nd section correct	B1
3^rd section correct and no “extras” on the sketch	B1
	(6)

Scheme	Marks
\(\dfrac{70 + 40}{2} \times v = 880\)	M1 A1
\(v = 880 \times \dfrac{2}{110} = 16\)	DM1 A1
	(4)
	(10 marks)