. A van of mass 900 kg is moving along a straight horizontal road.
At the instant when the speed of the van is v m s−1, the resistance to the
... [Show More] motion of the van is modelled as a force of magnitude (500 + 7v) N.
When the engine of the van is working at a constant rate of 18 kW, the van is moving along the road at a constant speed V m s−1
(a) Find the value of V.
(5)
Later on, the van is moving up a straight road that is inclined to the horizontal at an
1
angle θ , where sin θ =
21
At the instant when the speed of the van is v m s−1, the resistance to the motion of the van from non-gravitational forces is modelled as a force of magnitude (500 + 7v) N.
The engine of the van is again working at a constant rate of 18 kW.
(b) Find the acceleration of the van at the instant when v = 15
(4)
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*P66800A0228*
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*P66800A0328*
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*P66800A0428*
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(Total for Question 1 is 9 marks)
*P66800A0528*
2. Two particles, A and B, are moving in opposite directions along the same straight line on a smooth horizontal surface when they collide directly.
Particle A has mass 5m and particle B has mass 3m.
The coefficient of restitution between A and B is e, where e > 0
Immediately after the collision the speed of A is v and the speed of B is 2v.
Given that A and B are moving in the same direction after the collision,
(a) find the set of possible values of e.
(8)
Given also that the kinetic energy of A immediately after the collision is 16% of the kinetic energy of A immediately before the collision,
(b) find
(i) the value of e,
(ii) the magnitude of the impulse received by A in the collision, giving your answer in terms of m and v.
(6)
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