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M1 PPE Jan 2016
MEI Specification
Question paper
by
PiXL Maths Team
Time
Marks Available
1 Hour 30 Minutes
72
Commissioned by The PiXL Club Ltd.
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Section A (36 marks)
1
The diagram shows a velocity–time graph for a lift.
v ms-1
3
0
(a)
0
4
7
10
t seconds
Find the distance travelled by the lift.
(3)
(b)
Find the acceleration of the lift during the first 4 seconds of the motion.
(1)
2
3
A cyclist travels along a straight horizontal road. She accelerates uniformly from a speed of
2 m s–1 to 6 m s–1 as she travels 10 metres.
(a)
(i)
Show that the acceleration of the cyclist is 1.6 m s–2.
(2)
(ii)
Find the time that it takes the cyclist to travel this distance.
(2)
(b)
Model the cyclist as a particle of mass 65 kg. A constant resistance force of magnitude
35 N acts on the cyclist. A horizontal force of magnitude F newtons also acts on the
cyclist in the direction of motion. Find F.
(3)
4
Two children are holding the ends of a light, inextensible rope, which passes over a light, smooth
pulley. Initially Tom, who has a mass of 40 kg, is standing at ground level and Simon, who has a
mass of 60 kg, is on the edge of a fixed platform 2 metres above ground level. Model the two boys
as particles, one initially at ground level, and the other initially at a height of 2 metres. The rope is
taut.
Simon
Tom
2m
Simon steps off the platform and as he falls vertically, Tom rises vertically.
(a)
Assume that the rope remains taut while the boys are moving.
(i)
Show that the acceleration of each boy is 1.96 m s–2.
(ii)
Find the tension in the rope.
(4)
(2)
(b)
Find the total distance that Tom travels upwards.
(7)
5
Section B (36 marks)
6
A particle is launched from the point A on a horizontal surface, with a velocity of 22.4 m s−1 at an
angle θ above the horizontal, as shown in the diagram.
22.4 ms-1
C

A
B
After 2 seconds, the particle reaches the point C, where it is at its maximum height above the
surface.
(a)
Find the angle θ
(4)
(b)
Find the height of the point C above the horizontal surface.
(4)
(c)
The particle returns to the surface at the point B. Find the distance between A and B.
(3)
(d)
Find the length of time during which the height of the particle above the surface is
greater than 5 metres.
(7)
7
The constant forces F1 = (8i + 12j) newtons and F2 = (4i – 4j) newtons act on a particle.
No other forces act on the particle.
(a)
Find the resultant force acting on the particle.
(3)
(b) Given that the mass of the particle is 4 kg, show that the acceleration of the
particle is (3i + 2j) m s–2.
(3)
(c)
At time t seconds, the velocity of the particle is v m s–1.
(i)
When t = 20, v = 40i + 32j.
Show that v = –20i – 8j when t = 0.
(3)
(ii)
Write down an expression for v at time t.
(1)
(iii)
Find the times when the speed of the particle is 8 m s–1.
(8)