1. 1
   Two railway trucks are being shunted in a goods yard. Truck A, with a mass of 5000 kg, moves at 3 m/s towards a stationary truck B, which also has a mass of 5000 kg. Truck A collides with truck B and they couple together, moving off as one connected unit.

   (a)

   Calculate the momentum of truck A immediately before the collision.

   [1 mark]

   • A15000 kg m/s
   • B1667 kg m/s
   • C5003 kg m/s
   • D1500 kg m/s

   (b)

   What happens to the total momentum of the two trucks during the collision?

   [1 mark]

   • AIt is conserved — the total momentum is the same before and after the collision
   • BIt doubles as the trucks couple together
   • CIt is reduced to zero
   • DIt increases in proportion to the combined mass

   (c)

   Use conservation of momentum to calculate the common velocity of the two coupled trucks immediately after the collision.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   During a road-test crash, a car of mass 1200 kg travelling at 15 m/s collides with a barrier and is brought to rest in 0.15 s by its crumple zone and airbags.

   (a)

   Calculate the change in momentum of the car during the crash test.

   [1 mark]

   • A180 kg m/s
   • B1200 kg m/s
   • C18000 kg m/s
   • D90000 kg m/s

   (b)

   How does increasing the time taken for the collision, as the crumple zone and airbags do, affect the force experienced by the car's occupants?

   [1 mark]

   • AIt increases the force in direct proportion to the time
   • BIt decreases the force, since force is inversely proportional to the time taken for the momentum change
   • CIt has no effect on the force
   • DIt reverses the direction of the force only

   (c)

   Calculate the average force exerted on the car during the collision.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A kayaker sitting in a stationary kayak on a calm lake pushes against a jetty with her paddle in order to move away from it. The combined mass of the kayaker and kayak is 90 kg, and she exerts a force of 180 N on the jetty for 0.5 s.

   (a)

   Explain, using Newton's third law, why the kayak moves away from the jetty when the kayaker pushes against it with her paddle.

   [3 marks]

   (b)

   Calculate the velocity at which the kayak and kayaker move away from the jetty immediately after the push.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A road-safety engineer is investigating why modern cars are fitted with seatbelts and airbags, and is analysing a two-car collision in which a car of mass 1000 kg travelling at 12 m/s crashes into the back of a stationary car of mass 1000 kg. After the collision, both cars move off together at a common velocity.

   (a)

   Using ideas about momentum and force, explain how seatbelts and airbags reduce the risk of injury to occupants during a car collision.

   [6 marks]

   (b)

   Use conservation of momentum to calculate the common velocity of both cars immediately after the collision, and comment on what this calculation shows about the type of collision.

   [6 marks]

   Total for question 4: 12 marks

End of questions