Quantities in physics are either scalars or vectors.
(a) Use the correct answers from the box to complete the sentence.
acceleration direction distance speed time
Velocity is __________________________ in a given ________________ .
(2)
1
(b) Complete the table to show which quantities are scalars and which quantities are vectors.
Put one tick ( ) in each row.
The first row has been completed for you.
Quantity Scalar Vector
Momentum
Acceleration
Distance
Force
Time
(3)
(c) The diagram shows two supermarket trolleys moving in the same direction.
Trolley A is full of shopping, has a total mass of 8 kg and is moving at a velocity of 2 m / swith a kinetic energy of 16 J.
Trolley B is empty, has a mass of 4 kg and is moving at a velocity of 0.5 m / s with a kineticenergy of 0.5 J.
Page 1 of 21Wales+High+School
(i) Calculate the momentum of both trolley A and trolley B.
Give the unit.
______________________________________________________________
______________________________________________________________
Momentum of trolley A = _______________
Momentum of trolley B = _______________
Unit __________
(4)
(ii) The trolleys in the diagram collide and join together. They move off together.
Calculate the velocity with which they move off together.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
Velocity = _______________ m / s
(3)
(iii) In a different situation, the trolleys in the digram move at the same speeds as beforebut now move towards each other.
Calculate the total momentum and the total kinetic energy of the two trolleys beforethey collide.
______________________________________________________________
______________________________________________________________
Total momentum = _________________
______________________________________________________________
______________________________________________________________
Total kinetic energy = _______________ J
(2)
(Total 14 marks)
Page 2 of 21Wales+High+School
(a) A car driver sees the traffic in front is not moving and brakes to stop his car.
The stopping distance of a car is the thinking distance plus the braking distance.
(i) What is meant by the ‘braking distance’?
______________________________________________________________
______________________________________________________________
(1)
2
(ii) The braking distance of a car depends on the speed of the car and the braking force.
State one other factor that affects braking distance.
______________________________________________________________
______________________________________________________________
(1)
(iii) How does the braking force needed to stop a car in a particular distance depend onthe speed of the car?
______________________________________________________________
______________________________________________________________
(1)
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(b) Figure 1 shows the distance−time graph for the car in the 10 seconds before the driverapplied the brakes.
Use Figure 1 to calculate the maximum speed the car was travelling at.Show clearly how you work out your answer.
___________________________________________________________________
___________________________________________________________________
Maximum speed = ________________ m / s
(2)
(c) The car did not stop in time. It collided with the stationary car in front, joining the two carstogether.
Figure 2 shows both cars, just before and just after the collision.
Page 4 of 21Wales+High+School
(i) The momentum of the two cars was conserved.
What is meant by the statement ‘momentum is conserved’?
______________________________________________________________
______________________________________________________________
(1)
(ii) Calculate the velocity of the two joined cars immediately after the collision.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
Velocity = ___________________ m/s
(3)
(d) Since 1965, all cars manufactured for use in the UK must have seat belts.
It is safer for a car driver to be wearing a seat belt, compared with not wearing a seat belt, ifthe car is involved in a collision.
Explain why.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(4)
(Total 13 marks)
Page 5 of 21Wales+High+School
A paintball gun is used to fire a small ball of paint, called a paintball, at a target.
The figure below shows someone just about to fire a paintball gun.
The paintball is inside the gun.
(a) What is the momentum of the paintball before the gun is fired?
___________________________________________________________________
Give a reason for your answer.
___________________________________________________________________
___________________________________________________________________
(2)
3
(b) The gun fires the paintball forwards at a velocity of 90 m / s.
The paintball has a mass of 0.0030 kg.
Calculate the momentum of the paintball just after the gun is fired.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Momentum = ____________________ kg m / s
(2)
Page 6 of 21Wales+High+School
(c) The momentum of the gun and paintball is conserved.
Use the correct answer from the box to complete the sentence.
equal to greater than less than
The total momentum of the gun and paintball just after the gun is fired
will be ____________________________ the total momentum of the gun and
paintball before the gun is fired.
(1)
(Total 5 marks)
The figure below shows a skateboarder jumping forwards off his skateboard.
The skateboard is stationary at the moment the skateboarder jumps.
(a) The skateboard moves backwards as the skateboarder jumps forwards.
Explain, using the idea of momentum, why the skateboard moves backwards.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
4
Page 7 of 21Wales+High+School
(b) The mass of the skateboard is 1.8 kg and the mass of the skateboarder is 42 kg.
Calculate the velocity at which the skateboard moves backwards if the skateboarder jumpsforwards at a velocity of 0.3 m / s.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Velocity of skateboard = ____________________ m / s
(3)
(Total 6 marks)
(a) In any collision, the total momentum of the colliding objects is usually conserved.
(i) What is meant by the term ‘momentum is conserved’?
______________________________________________________________
______________________________________________________________
(1)
5
(ii) In a collision, momentum is not always conserved.
Why?
______________________________________________________________
______________________________________________________________
(1)
Page 8 of 21Wales+High+School
(b) The diagram shows a car and a van, just before and just after the car collided with the van.
(i) Use the information in the diagram to calculate the change in the momentum of thecar.
Show clearly how you work out your answer and give the unit.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
Change in momentum = _________________________
(3)
(ii) Use the idea of conservation of momentum to calculate the velocity of the van when itis pushed forward by the collision.
Show clearly how you work out your answer.
______________________________________________________________
______________________________________________________________
______________________________________________________________
Velocity = _________________________ m/s forward
(2)
(Total 7 marks)
(a) Complete the following sentence.
The momentum of a moving object has a magnitude, in kg m/s,
and a _________________________ .
(1)
6
Page 9 of 21Wales+High+School
(b) A car being driven at 9.0 m/s collides with the back of a stationary lorry.The car slows down and stops in 0.20 seconds. The total mass of the car and driver is1200 kg.
Calculate the average force exerted by the lorry on the car during the collision.
Show clearly how you work out your answer.
___________________________________________________________________
___________________________________________________________________
Force = _________________________ N
(2)
(c) Within 0.04 s of the car hitting the back of the lorry, the car driver's airbag inflates.The airbag deflates when it is hit by the driver’s head.
Use the idea of momentum to explain why the airbag reduces the risk of the drivesustaining a serious head injury.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(Total 6 marks)
Page 10 of 21Wales+High+School
The arrows in the diagram represent the horizontal forces acting on a motorbike at one momentin time.
7
(a) The mass of the motorbike and rider is 275 kg.
Calculate the acceleration of the motorbike at this moment in time.
Show clearly how you work out your answer.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Acceleration = ______________________________ m/s2
(3)
Page 11 of 21Wales+High+School
(b) A road safety organisation has investigated the causes of motorbike accidents.
The main aim of the investigation was to find out whether there was any evidence thatyoung, inexperienced riders were more likely to be involved in an accident than older,experienced riders.
Data obtained by the organisation from a sample of 1800 police files involving motorbikeaccidents, is summarised in the table.
Size of motorbikeengine
Percentage of allmotorbikes sold
Total number inthe sample of 1800
accident files
up to 125 cc 36 774
126 to 350 cc 7 126
351 to 500 cc 7 162
over 500 cc 50 738
Most of the motorbikes with engines up to 125 cc were ridden by young people.The motorbikes with engines over 500 cc were ridden by older, more experienced riders.
(i) In terms of the main aim of the investigation, is this data valid?
Draw a ring around your answer. NO YES
Explain the reason for your answer.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
Page 12 of 21Wales+High+School
(ii) The organisation concluded that:
“Young, inexperienced riders are more likely to be involved in a motorbike accidentthan older, experienced riders”.
Explain how the data supports this conclusion.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
(c) Of particular concern to motorbike riders is the design of steel crash barriers. Riders fallingoff and sliding at high speed into a steel support post are often seriously injured.
One way to reduce the risk of serious injury is to cover the post in a thick layer of highimpact polyurethane foam.
(i) Use the ideas of momentum to explain how the layer of foam reduces the risk ofserious injury to a motorbike rider sliding at high speed into the support post.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
Page 13 of 21Wales+High+School
(ii) Crash barrier tests use dummies that collide at 17 m/s with the barrier. Each testcosts about £12 000. New safety devices for crash barriers are tested many times tomake sure that they will improve safety.
Do you think that the cost of developing the new safety devices is justified?
Draw a ring around your answer. NO YES
Give a reason for your answer.
______________________________________________________________
______________________________________________________________
(1)
(Total 11 marks)
Page 14 of 21Wales+High+School
Mark schemes
(a) speed
must be in correct order1
direction1
1
(b)
Quantity Scalar Vector
Momentum
Acceleration
Distance
Force
Time
any three correct scores 2 marks
any two correct scores 1 mark
only one correct scores zero3
(c) (i) 16 and 2
16 or 2 scores 2 marks
allow 1 mark for correct substitution, ie
8 × 2
or
4 × 0.53
kg m / s or N s1
(ii) 1.5 (m / s)ortheir pA + pB = 12 × v correctly calculated
allow 2 marks for correct substitution, ie
18 = 12 × v
or
their pA + pB = 12 × v
18 or their pA + pB scores 1 mark if no other mark awarded3
Page 15 of 21Wales+High+School
(iii) 14 (kg m / s)ortheir pA - pB
1
16.5 (J)1
[14]
(a) (i) distance travelled under the braking force
accept distance travelled between applying the brakes and stopping1
(ii) any one from:• icy / wet roads
accept weather (conditions)• (worn) tyres• road surface
accept gradient of road• mass (of car and passengers)
accept number of passengers• (efficiency / condition of the) brakes.
friction / traction is insufficient1
(iii) greater the speed the greater the braking force (required)
must mention both speed and force1
2
(b) 22.5
allow 1 mark for showing correct use of the graph with misreadfigures
or
for showing e.g. 90÷4
an answer 17 gains 1 mark
any answer such as 17.4 or 17.5 scores 02
Page 16 of 21Wales+High+School
(c) (i) momentum before = momentum afteror(total) momentum stays the same
accept no momentum is lost
accept no momentum is gained
ignore statements referring to energy1
(ii) 5
allow 2 marks for correctly obtaining momentum before as
12 000
or
allow 2 marks for
1500 × 8 = 2400 × v
or
allow 1 mark for a relevant statement re conservation of momentum
or
allow 1 mark for momentum before = 1500 × 83
(d) the seat belt stretches1
driver takes a longer (impact) time to slow down and stop (than a driver hitting a hardsurface / windscreen / steering wheel)
1
for the (same) change of momentum
accept so smaller deceleration / negative acceleration1
a smaller force is exerted (so driver less likely to have serious injury than driverwithout seat belt)orthe seat belt stretches (1)
do not accept impact for force
driver travels a greater distance while slowing down and stopping (than a driverhitting a hard surface / windscreen / steering wheel) (1)
for (same) amount of work done (1)
accept for (same) change of KE
a smaller force is exerted (so driver less likely to have serious injury than driverwithout seat belt) (1)
do not accept impact for force1
[13]
Page 17 of 21Wales+High+School
(a) Zero / 0
Accept none
Nothing is insufficent1
velocity / speed = 0
accept it is not moving
paintball has not been fired is insufficient1
(b) 0.27
allow 1 mark for correct substitution, ie p = 0.003(0) × 90 providedno subsequent step
2
(c) equal to1
[5]
3
(a) momentum before (jumping) = momentum after (jumping)
accept momentum (of the skateboard and skateboarder) isconserved
1
before (jumping) momentum of skateboard and skateboarder is zero
accept before (jumping) momentum of skateboard is zero
accept before (jumping) total momentum is zero1
after (jumping) skateboarder has momentum (forwards) so skateboard must have(equal) momentum (backwards)
answers only in terms of equal and opposite forces are insufficient1
(b) 7
accept –7 for 3 marks
allow 2 marks for momentum of skateboarder equals 12.6
or
0 = 42 × 0.3 + (1.8 × –v)
or
allow 1 mark for stating use of conservation of momentum3
[6]
4
(a) (i) momentum before = momentum after
accept no momentum is lost
accept no momentum is gained
or(total) momentum stays the same
1
5
Page 18 of 21Wales+High+School
(ii) an external force acts (on the colliding objects)
accept colliding objects are not isolated1
(b) (i) 9600
allow 1 mark for correct calculation of momentum before or after ie12000 or 2400orcorrect substitution using change in velocity = 8 m/sie 1200 × 8
2
kg m/sorNs
this may be given in words ratherthan symbolsdo not accept nS
1
(ii) 3 or their (b)(i) ÷ 3200 correctly calculated
allow 1 mark for stating momentum before = momentum after
or
clear attempt to use conservation of momentum2
[7]
(a) direction16
(b) 54 000
allow 1 mark for calculating and identifying momentum as 10 800
or
allow 1 mark for correct substitution into second equation
2
ie
(c) increases the time taken (for head) to stop
accept increases impact time
do not accept reference to slowing down time unless qualified1
decreases rate of change in momentum
accept reduces acceleration / deceleration
accept increases the time taken to reduce momentum to zero isworth 2 marks
reduces momentum is insufficient1
Page 19 of 21Wales+High+School
reduces the force (on the head)1
[6]
(a) 4.2
2 marks for correct substitution and transformation, ie 1155/275
allow 1 mark for correct resultant force with a subsequent incorrectmethod, ie 1155
allow 1 mark for an incorrect resultant force with a subsequentcorrect method,
eg answers of 7.27 or 10.34 gain 1 mark3
7
(b) (i) YES
marks are for the explanation
any two from:
• data (from police files) can be trusted
• data answers the question asked
allow a conclusion can be made from the data
• large sample used
NO
any two from:
• the sample is not representative
• the sample size is too small
• accident files do not indicate age / experience of riders
an answer YES and NO can score 1 mark from each set of markpoints
2
(ii) more accidents with motorbikes up to 125 cc
accept for 2 marks an answer in terms of number of under 125 cc toaccidents ratio compared correctly with number of over 500 cc toaccidents ratio
1
even though there are fewer of these bikes than bikes over 500 cc1
(c) (i) increases the time taken to stop
accept increases collision time1
Page 20 of 21Wales+High+School
decreases rate of change in momentum
accept reduces acceleration / deceleration
reduces momentum is insufficient1
accept
reduces the force (on the rider)1
(ii) YES
any sensible reason, eg:
the mark is for the reason
• cannot put a price on life / injury
accept may save lives
• fewer (serious) injuries
accept reduces risk of injury
• reduces cost of health care / compensation
NO
any sensible suggestion, eg:
• money better spent on …
needs to be specific
• total number of riders involved is small1
[11]
Page 21 of 21Wales+High+School