Name: _______________________________________________

P2 Topic 3 – Motion and forces Foundation.

Date:

Time: 30 minutes

Total marks available: 30

Total marks achieved: ______

Questions Q1.

(a) Here is the velocity-time graph for a car for the first 20 s of a journey.

(i) Calculate the change in velocity of the car during the first 5 s.

(1)

.............................................................................................................................................. (ii) Calculate the acceleration of the car during the first 5 s.

(2)

acceleration = . . . . . . . . . . . . . . . . . . . . . . m/s2 (iii) State the size of the resultant force between 10 s and 15 s

(1)

.............................................................................................................................................. (b) The mass of a car is 1200 kg.

Calculate the resultant force on the car required to produce an acceleration of 0.8 m/s2. (2)

..............................................................................................................................................

*(c) A car, travelling at 20 m/s, with just the driver inside takes 70 m to stop in an emergency. The same car is then fully loaded with luggage and passengers as well as the driver.

Explain why it will take a different distance to stop in an emergency from the same speed. (6)

.............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

(Total for Question = 12 marks)

Q2. Forces and motion

(a) The diagram shows some of the forces acting on an airliner in flight. The airliner is flying at a constant height above the ground. Only two of the forces acting on the airliner are shown.

(i) Use words from the box to label the diagram. (2)

thrust drag lift weight

(ii) Draw another arrow on the diagram to show the friction forces acting on the airliner.

(1) (iii) The airliner is accelerating. Which of these statements is correct for the accelerating airliner?

Put a cross ( ) in the box next to your answer. (1)

A the friction forces are zero

B the thrust is greater than the friction forces

C the thrust is smaller than the friction forces

D the thrust is the same size as the friction forces (b) This is a photograph of one of the airliner’s jet engines.

(i) When the fuel burns, hot exhaust gases are forced backwards out of the engine. Explain why this creates a forward thrust.

(2) .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

(ii) When the airliner is taking off it accelerates along the runway. It starts from rest and takes off 50 seconds later. Its speed at take off is 60 m/s. Calculate its average acceleration along the runway.

(2)

acceleration = ...................................... m/s2 (iii) If the same airliner carries fewer passengers but uses the same engine thrust, it can take off in a shorter time. Explain why.

(2)

.............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

Q3.

A crane is lifting a heavy block from the ground to the top of a building.

This is the velocity/time graph for the block as it travels upwards.

(i) For how many seconds is the block moving at a constant velocity?

(1)

.............................................................................................................................................. This diagram shows one of the forces acting on the block.

(ii) Draw an arrow on the diagram to represent the weight of the block.

(1)

(iii) Complete the sentence by putting a cross ( ) in the box next to your answer. When the block is moving upwards at a constant velocity, the resultant force on the block is

(1)

A upwards and equal to its weight

B downwards and equal to its weight

C upwards and more than its weight

D zero (iv) Use the velocity/time graph to calculate the acceleration of the block during the first 2 s. State the unit.

(3)

.............................................................................................................................................. (v) Explain why the upward force from the cable during the first 2 s is greater than the upward force for the next 4 s.

(2)

.............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

Examiner's Report Q1. aiii Candidates should be aware that if they are asked to state a value then a calculation is not necessary. This question asked candidates to 'state the size' of the resultant force between 10s and 15s. The graph shows that the car had a constant velocity during this time and so the resultant force must be zero.

Results Plus: Examiner Comments

The answer should be simply 0.

Results Plus: Examiner Tip You do not need to do a calculation if you are simply asked to 'state the size' of something.

ai-ii For the first part of this question (i), candidates needed to subtract the starting velocity (0) from the velocity at 5s (8 m/s) to arrive at an answer of 8 m/s. Many candidates calculated the acceleration in this part by finding the gradient of the line. In the second part (ii), candidates needed to divide the change in velocity in part (i) by the time taken (5s) to find the acceleration (1.6 m/s2). Provided that working was shown, examiners allowed full credit for an error carried forward from (i) into (ii). Although the answer to part (i) is incorrect, the candidate has carried on to use the value to calculate acceleration and has shown the working. The examiner could clearly see that the candidate knows how to find acceleration and awarded 2 marks for part (ii).

Results Plus: Examiner Comments Candidates need to be clear about the difference between 'change in velocity' and 'rate of change in velocity' (ie acceleration).

Results Plus: Examiner Tip 'Calculate' does not always mean that you have to multiply or divide. It can also mean add or subtract.

b This was a straightforward calculation for most candidates. The most common error seemed to be incorrect use of the calculator by carrying out a division of 1200 by 0.8 to produce a result of 1500. As usual, candidates could score 1 mark if the substitution was correctly shown.

Results Plus: Examiner Comments This clearly laid out response scored 2 marks.

A mark was given for substituting the correct values into the equation.

Results Plus: Examiner Comments The expression 1200 Kg x 0.8 is correct for one mark. Unfortunately the candidate seems to have used the divide function on the calculator and so could not get the second mark.

Results Plus: Examiner Comments The candidate may have made the same mistake and pressed divide rather than multiply on the calculator. Unfortunately, there was no working shown and so no marks were scored.

Results Plus: Examiner Tip Always show your working.

c Most candidates realised that the extra passengers and luggage would increase the overall mass

of the car. However, very many expressed this as an increase in weight rather than mass. This seemed to lead them towards considering downwards forces on the road and, very often, increase in friction. They then drew the conclusion that this would make the car stop more quickly in an emergency. There was a widespread misunderstanding that it was friction between the tyres and the road which was responsible for stopping the car when the brakes were applied. It was surprising that a large number of candidates thought that a heavily loaded car could stop more quickly than one with just the driver. Candidates who correctly used the term 'increase in mass' very often went on to reason that the car would take a longer time to come to halt. This was sometimes nicely expressed in terms of momentum or kinetic energy and sometimes expressed in terms of forces and rate of change of velocity. It was sometimes difficult for the examiner to decide whether 'takes longer to stop' referred to a longer time or a greater distance. There were quite a few candidates who suggested that the passengers might distract the driver. They often went on to give a good description of how this could affect overall stopping distance by increasing the thinking distance. Examiners gave credit for this.

Results Plus: Examiner Comments This answer makes a correct statement about the mass or weight increasing when the car is fully loaded. This is a level 1 response. It then goes on to consider resistance and forces pulling the car down to arrive at a conclusion that the car will stop quicker than an unloaded car. This is incorrect and so cannot reach level 2. It scored only 2 marks.

Results Plus: Examiner Comments The candidate links the increase in mass with taking 'longer to stop'. It is not clear whether this is a longer time or a longer distance. The answer goes on to describe air resistance and gravity which is not relevant in this situation. It then goes on to mention resultant forces, but, once again, this is not in the correct context. The examiner ignored the second and third sentences. The candidate eventually goes on to state that the lighter car takes a shorter time to stop without mentioning distance. This is a good level 2 response but does not quite make the links clear enough to reach level 3. The quality of written communication is appropriate. It scored 4 marks.

Results Plus: Examiner Comments Although it not clear what force is being referred to, the answer makes very good points about an increase in mass resulting in a longer time to stop and so a longer distance travelled. This is a level 3 response. The quality of written communication is appropriate for this level. It scored all 6 marks.

Q2. No Examiner's Report available for this question Q3.

(i)

A majority gave the correct answer but some gave 17 or 18 which was unacceptable given such a clear graph.

(ii)

Most were awarded the mark for this question. The arrow shown in the diagram should have cued candidates into starting their arrow from the centre. The most common error was starting the arrow from a point too far below the centre of the block.

(iv)

Many candidates were able to substitute and evaluated correctly. However some chose to rearrange the equation and so gave the answer as 6. A common error was to give incorrect units for acceleration, with m/s being the most common but some seemed to choose any unit that came to mind.

60% of candidates scored either two or three marks for this question.

One of the responses scoring full marks.

Results Plus: Examiner Comments Well set out responses usually scored most of the marks.

Only two marks.

Results Plus: Examiner Comments The most common reason for losing a mark was to give an incorrect unit for acceleration.

A response scoring one mark.

Results Plus: Examiner Comments This candidate scored one mark for the correct unit.

(v)

It was disappointing that so many candidates were unable to correctly interpret the velocity/ time graph. Most scored one mark for either saying that that the block accelerated for the first two seconds and then travelled at constant speed for the next four. Some interpreted it as a distance-time graph and assumed that the constant velocity section represented the box being stationary and the final deceleration section meaning the box is being lowered. Others spoke of the weight of the box changing or more force being needed to start lifting objects.

A two mark response

Results Plus: Examiner Comments This was the most common type of response scoring two marks.

A typical response gaining one mark.

Results Plus: Examiner Comments One mark for the idea that velocity is constant after the first two seconds.

Mark Scheme Q1.

Answer Acceptable

answers Mark

(a)(i) 8 – 0 (m/s) 8 (1)

(a)(ii) substitution 8 / 5 (1) evaluation (1) 1.6 (m/s2)

ecf from (i) full marks for correct answer (or ecf) with no working shown.

(2)

(a)(iii) 0 Nil / nothing / zero / none (no mark for no response) (1)

(b) substitution F = 1200 × 0.8 (1)

full marks for correct answer with no working shown.

(2)

evaluation (1) 960 (N)

Indicative Content Mark

QWC *(c) an explanation linking some of the following points: compared to a car with just the driver, a fully loaded car will

have a greater mass / be heavier

greater kinetic energy / momentum

experience the same braking force (when brakes are applied)

require a greater braking force (than available) to stop (in the same distance)

have a smaller acceleration / deceleration

take a longer time to come to rest (from given speed)

travel greater distance in this time

needs to do more work with same amount of force

use of relevant equations such as F = ma, work done = F × d

consequence of driver distractions (6)

Level 0 No rewardable content

1 1 - 2

a limited explanation using one idea from the indicative content eg fully loaded car is heavier.

in answer communicates ideas using simple language and uses limited scientific terminology

spelling, punctuation and grammar are used with limited accuracy

2 3 - 4

a simple explanation which links ideas from the indicative content eg it is heavier and so it takes a longer distance to stop

the answer communicates ideas showing some evidence of clarity and organisation and uses scientific terminology

appropriately

spelling, punctuation and grammar are used with some accuracy

3 5 - 6

a detailed explanation which links several ideas from the indicative content e.g. It has more momentum and so it will take a longer time to stop. This means that it will travel a further distance. The answer communicates ideas clearly and coherently uses a range of scientific terminology accurately

spelling, punctuation and grammar are used with few errors

Q2.

Question Number

Answer Acceptable answers Mark

(a)(i) • thrust (to right) (1) • weight (downwards) (1)

(2)

Question Number

Answer Acceptable answers Mark

(a)(ii) horizontal arrow drawn pointing to the left and starting from some point on the ‘airliner’ (need not have a label)

both start and end of arrow could be on the airliner

(2)

Question Number

Answer Acceptable answers Mark

(a)(iii) B (1)

Question Number

Answer Acceptable answers Mark

(b)(i) An explanation linking two of the following points • there is a reaction force (1) • (which) acts on the engine / airliner (1) • (must be) in the opposite direction (to that on the gases) (1)

(2)

Question Number

Answer Acceptable answers Mark

(b)(ii) substitution (1) 60 ÷ 50 evaluation (1) 1.2 (m/s2)

give full marks for correct answer, no working (2)

Question Number

Answer Acceptable answers Mark

(b)(iii) An explanation linking two of the following points • weight /mass will

take off at lower velocity / speed / reduces take off speed sooner (2)

be reduced (1) • (so) greater acceleration (from same force) (1) • (therefore) will need less lift to achieve take off (1)

Q3.

Answer Acceptable

answers Mark

(i) 16 (s) (1)

Sixteen/ sixteen seconds/ 16 s/ 16 seconds

(1)

(ii) Downward arrow starting at centre of the block (1)

Mark by eye ie ruler not required. Accept freehand lines and gaps between dot and line less than half the distance between dot and bottom of block by eye. Accept lines that are not quite vertical

(1)

(iii) D zero (1)

(iv) Substitution 3 / 2 (1) Evaluation 1.5 (1) Unit m/s2 (1)

ms-2 or m/s/s bald 1.5 × 10n m/s2 gains 2 marks eg bald 150 = 1 mark (BOD for correct substitution) 150 m/s2 gains 2 marks give full marks for correct numerical answer, 1.5 m/s2 even if no working

(3)

(v) An explanation to include two of the following points

(At first/in first 2 seconds Block is) accelerating (1)

Which requires a (resultant) force (1)

In addition to the force needed to balance the weight of the block (1)

(In next 4

(block is) speeding up/increasing velocity there is an unbalanced force/ forces are not balanced (Because) speed is steady

(2)

seconds) forces are balanced (1)

(Because) velocity is constant (1)