Scalars & Vectors (AQA AS Maths): Revision Note
Exam code: 7356
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Scalars & vectors
Mechanics uses a variety of different scalar and vector quantities.
What are scalars?
Scalars are quantities without direction, they only have a size (magnitude)
e.g. a speed of 7 m/s, a distance of 5 m, a time of 15 s or a mass of 12 kg
Scalars can only be positive- you can’t have a negative distance or speed!
What are vectors?
Vectors are quantities which also have a direction, this is what makes them more than just a scalar
e.g. two objects with velocities of 7 m/s and ‑7 m/s are travelling at the same speed but in opposite directions
Vector quantities can have positive or negative components
Some examples of vector quantities you may come across are displacement, velocity, acceleration, force/weight, momentum
Displacement is the distance moved in a given direction from a starting point
Velocity is a speed in a given direction (displacement over time)
Acceleration is the change in velocity over time
Vector quantities of displacement, velocity and acceleration
Worked Example
State whether each of the following is a scalar or a vector quantity.
a) A speed boat travels at 3m/s on a bearing of 052o
b) A garden is 1.7 m wide
c) A car accelerates at 5.4 ms-2
d) A film lasts 2 hours 17 minutes
e) An athlete runs at an average speed of 10.44 ms-2
f) A ball rolls forwards 60 cm before stopping
Examiner Tips and Tricks
Make sure you fully understand the definitions of all the words in this section so that you can be clear about what your exam question is asking of you
Vectors appear in bold (non-italic) font in textbooks, on exam papers, etc (i.e. F, α ) but in handwriting should be underlined (i.e. F , α )
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