# 2.10 Summary

• Displacement (s) is straight line distance in a particular direction from a chosen reference point
• Distance is not necessarily measured along a straight line and takes no account of direction
• Speed is the rate of change of distance with time i.e. speed = distance travelled/time taken s = Δd/Δt
• Velocity is the rate of change of displacement with time i.e. velocity = change in displacement/ time taken v = Δs/Δt
• Acceleration is the rate of change of velocity with time i.e acceleration = change in velocity/ time taken a = Δv/Δt
• The three equations above are often written without the Δ symbols e.g. a = v/ t (This implies that the initial values are zero)
• The speed, velocity and acceleration of an object can vary over time so the equations above can be used to calculate either average values or instantaneous values ( i.e the value over a very short time interval)
• Displacement, velocity and acceleration are vector quantities - they have direction as well as magnitude
• Vectors can be represented with arrows whose length represents magnitude and they point in the direction that the vector is acting
• Distance and speed are scalar quantities - they have magnitude only
• Because there are a limited number of letters available some symbols are used to represent more than one quantity. The meaning should be clear from the context and alternative symbols can be used in situations where there could be confusion. e.g for an example that involves both speed (s) and displacement (s) then (x) could be used for displacement etc.

For one dimensional motion:

• The directional nature of vectors can be represented with + and - signs
• When there is no change in direction distance = magnitude of displacement and speed = magnitude of velocity
• Instantaneous value of speed = magnitude of instantaneous velocity