5.1 Scalars and vectors
9 exam questions worth 17 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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Which of these is a vector quantity?
Choose one answer.
Correct Not quite: the answer is Velocity
Mark scheme
C: Velocity
Model answer
Velocity (C).
Which of these is a scalar quantity?
Choose one answer.
Correct Not quite: the answer is Time
Mark scheme
D: Time
Model answer
Time (D).
State the difference between a scalar and a vector.
Mark scheme
a scalar has size / magnitude only (1); a vector has size and direction (1)
Model answer
A scalar has only a size, whereas a vector has both a size and a direction.
State the difference between speed and velocity.
Mark scheme
speed has no direction / is a scalar (1); velocity is speed in a given direction / is a vector (1)
Model answer
Speed is a scalar with only a size. Velocity is a vector: it is the speed in a given direction.
A person walks 6 m east and then 8 m north. Calculate (a) the distance walked and (b) the magnitude of the displacement.
Mark scheme
(a) 6 + 8 = 14 m (1); (b) √(6² + 8²) (1); 10 m (1)
Model answer
(a) Distance = 6 + 8 = 14 m. (b) Displacement = √(6² + 8²) = √100 = 10 m.
A cyclist rides once around a circular track and finishes where she started. State her displacement and explain your answer.
Mark scheme
0 m (1); she finishes at the start point / the straight-line distance between start and finish is zero (1)
Model answer
Her displacement is 0 m, because she finishes at the same place she started.
Two cars travel at 20 m/s. One goes north and the other goes south. Explain whether they have the same speed or the same velocity.
Mark scheme
same speed (1); different velocity because the directions are different (1)
Model answer
They have the same speed of 20 m/s, but different velocities, because they are moving in opposite directions.
A student runs at a constant speed of 4 m/s around a circular track. Explain why her velocity is not constant.
Mark scheme
velocity is a vector / depends on direction (1); the direction of motion is constantly changing (1)
Model answer
Velocity includes direction, and as she runs around the track her direction is always changing, so her velocity changes even though her speed does not.
Explain why mass is a scalar quantity but weight is a vector quantity.
Mark scheme
mass has size only / no direction (1); weight is a force which acts in a direction (downwards) (1)
Model answer
Mass has only a size. Weight is a force, which has a direction (towards the centre of the Earth).
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