surname names
Number Number
Paper
Further Mathematics
� �
Advanced
PAPER 3C: Further Mechanics 1
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Answer all questions and ensure that your answers to parts of questions are clearly labelled.
–You
there mayshow
should be more space than
sufficient youto
working need.
make your methods clear.
• Answers without working may not gain full credit. –2
and give
your answer to either 2 significant figures or 3 significant figures.
Information
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• There are 8 questions in this question paper. The total mark for this paper is 75.
– use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. A particle A has mass 4m and a particle B has mass 3m. The particles are moving along
the same straight line on a smooth horizontal table. The particles are moving in opposite
directions towards each other when they collide directly.
As a result of the collision, the direction of motion of each particle is reversed.
Immediately before the collision, the speed of A is u and the speed of B is ku, where k
is a constant.
Immediately after the collision, the speed of A is 2v and the speed of B is 3v.
The magnitude of the impulse received by A in the collision is 20mv.
(a) Find u in terms of v only.
(3)
(b) Find the exact value of k.
(3)
,Question 1 continued
(Total for Question 1 is 6 marks)
, 2. A van of mass 900 kg is moving along a straight horizontal road.
When the speed of the van is v ms1, the resistance to the motion of the van is
modelled as a force of magnitude 50v N.
The engine of the van is working at a constant rate of 12 kW.
At the instant when the speed of the van is V ms1, the acceleration of the van
is 0.2 ms2
Using the model,
(a) find the value of V.
(4)
Later on, the van is moving up a straight road that is inclined at an angle α to the
1
horizontal, where sin α . When the speed of the van is v ms1, the resistance
12
to the motion of the van from non-gravitational forces is modelled as a force of
magnitude 50v N.
When the van has constant speed U ms−1, the engine of the van is working at a constant
rate of 15 kW.
Using the model,
(b) find the value of U.
(4)
Number Number
Paper
Further Mathematics
� �
Advanced
PAPER 3C: Further Mechanics 1
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Answer all questions and ensure that your answers to parts of questions are clearly labelled.
–You
there mayshow
should be more space than
sufficient youto
working need.
make your methods clear.
• Answers without working may not gain full credit. –2
and give
your answer to either 2 significant figures or 3 significant figures.
Information
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• There are 8 questions in this question paper. The total mark for this paper is 75.
– use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. A particle A has mass 4m and a particle B has mass 3m. The particles are moving along
the same straight line on a smooth horizontal table. The particles are moving in opposite
directions towards each other when they collide directly.
As a result of the collision, the direction of motion of each particle is reversed.
Immediately before the collision, the speed of A is u and the speed of B is ku, where k
is a constant.
Immediately after the collision, the speed of A is 2v and the speed of B is 3v.
The magnitude of the impulse received by A in the collision is 20mv.
(a) Find u in terms of v only.
(3)
(b) Find the exact value of k.
(3)
,Question 1 continued
(Total for Question 1 is 6 marks)
, 2. A van of mass 900 kg is moving along a straight horizontal road.
When the speed of the van is v ms1, the resistance to the motion of the van is
modelled as a force of magnitude 50v N.
The engine of the van is working at a constant rate of 12 kW.
At the instant when the speed of the van is V ms1, the acceleration of the van
is 0.2 ms2
Using the model,
(a) find the value of V.
(4)
Later on, the van is moving up a straight road that is inclined at an angle α to the
1
horizontal, where sin α . When the speed of the van is v ms1, the resistance
12
to the motion of the van from non-gravitational forces is modelled as a force of
magnitude 50v N.
When the van has constant speed U ms−1, the engine of the van is working at a constant
rate of 15 kW.
Using the model,
(b) find the value of U.
(4)
