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Practise 20 exam-style questions on Scalar and vector quantities for AQA GCSE Physics. Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
State what is meant by a vector quantity.
A vector quantity has both magnitude (size) and an associated direction.
To describe a vector fully you must give its size and its direction, for example '20 N downwards' or '15 m/s north'. Force, velocity, displacement, acceleration and momentum are all vectors.
has magnitude / size
and (an associated) direction
The diagram shows the two horizontal forces, A and B, acting on a sledge. The arrows are drawn to the same scale.
Force A is 30 N.
Determine the size of force B. Give a reason for your answer.
Force B is 10 N. The length of each arrow represents the size of the force, and arrow B is one-third as long as arrow A, so force B = 30 N ÷ 3 = 10 N.
When arrows are drawn to the same scale, comparing their lengths compares the sizes of the forces. The arrows also point in opposite directions, which shows the two forces act in opposite directions.
10 N
correct answer with no working scores full marks
arrow B is one-third of the length of arrow A, and the length of an arrow represents the magnitude of the force
allow arrow B is a third as long as A
A student represents two forces, P and Q, acting on an object as arrows on squared paper. The diagram shows the arrows, drawn to scale.
Determine the magnitude of force P and the magnitude of force Q.
Describe the direction of force Q compared with the direction of force P.
Each square represents 5 N.
Arrow P is 6 squares long, so P = 6 × 5 N = 30 N.
Arrow Q is 4 squares long, so Q = 4 × 5 N = 20 N.
P acts horizontally to the right and Q acts vertically upwards, so Q is at right angles (90°) to P.
In a scale drawing, count the squares along each arrow and multiply by the scale. The direction of each arrow shows the direction of each force, which is what makes force a vector quantity.
P = 30 N
6 squares × 5 N; correct answer with no working scores full marks
Q = 20 N
4 squares × 5 N
Q acts at right angles / 90° to P
allow P is to the right and Q is upwards / perpendicular
Two identical trolleys, each of mass 2.0 kg, move towards each other along a straight track. Each trolley has a speed of 3.0 m/s.
Calculate the total momentum of the two trolleys.
Explain your answer.
Momentum of each trolley = mass × velocity = 2.0 kg × 3.0 m/s = 6.0 kg m/s.
Momentum is a vector, and the trolleys move in opposite directions. Taking one direction as positive, one trolley has momentum +6.0 kg m/s and the other −6.0 kg m/s.
Total momentum = 6.0 + (−6.0) = 0 kg m/s.
Vectors in opposite directions must be given opposite signs before they are added. Adding the sizes to get 12 kg m/s ignores direction and treats momentum as if it were a scalar. A total momentum of zero does not mean nothing is moving - it means the momenta in the two directions are equal and opposite.
momentum of each trolley = 2.0 × 3.0 = 6.0 kg m/s
an answer of 0 with a correct explanation scores 4 marks
momentum is a vector and the trolleys move in opposite directions
so one momentum is +6.0 kg m/s and the other is −6.0 kg m/s / total = 6.0 + (−6.0)
total momentum = 0
do not accept 12 kg m/s
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