Scalars & Vectors (Cambridge International AS Mathematics)

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 052^o

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^-1

f) A ball rolls forwards 60 cm before stopping

Answer:

Exam Hint

• 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 *)