Exam Questions & Solutions
Time: 1 hour 30 minutes
Total marks: 60
Instructions:
Show all working.
Answers should be exact unless otherwise stated.
Calculators may be used.
Take .
Question 1 — Kinematics (5 marks)
A particle moves in a straight line with velocity
v(t) = 6t - 4 \quad \text{m/s},
(a) Find the displacement of the particle between and . (3)
(b) Determine the time when the particle is instantaneously at rest. (2)
Question 2 — Forces & Newton’s Laws (6 marks)
, A block of mass is pulled up a rough plane inclined at to the horizontal by a force of
acting parallel to the plane.
The coefficient of friction between the block and the plane is .
(a) Draw a labelled force diagram for the block. (2)
(b) Find the acceleration of the block up the plane. (4)
Question 3 — Motion under Gravity (7 marks)
A particle is projected vertically upwards from ground level with speed .
(a) Find the maximum height reached. (3)
(b) Determine the time during which the particle is above a height of . (4)
Question 4 — Connected Particles (7 marks)
Particles and , of masses and respectively, are connected by a light inextensible string
passing over a smooth pulley.
Particle rests on a smooth horizontal table and hangs freely.
(a) Determine the acceleration of the system. (4)
(b) Find the tension in the string. (3)
Question 5 — Work, Energy & Power (8 marks)