Distance, displacement, speed, velocity and acceleration, the difference between scalar and vector quantities, and how to use and rearrange the speed and acceleration equations.

What this dot point is asking

CCEA Double Award wants you to tell the difference between scalar and vector quantities, to define distance, displacement, speed, velocity and acceleration, and to use and rearrange the equations that link them. Speed and acceleration calculations appear in every Unit P1 paper, so the equations and units must be automatic.

Scalars and vectors

Distance is how far an object has travelled, regardless of direction. Displacement is the straight-line distance from start to finish in a stated direction. If you walk 3 m east and then 3 m west, the distance is 6 m but the displacement is 0 m.

Speed and velocity

Speed is how fast distance is covered. Velocity is speed in a stated direction, so it is a vector.

The average speed uses the total distance over the total time; the instantaneous speed is the speed at one moment, for example the reading on a speedometer.

Acceleration

Acceleration is the rate of change of velocity. An object accelerates if it speeds up, slows down (a negative acceleration, or deceleration) or changes direction.

Examples in context

Example 1. A lift. A lift starting from rest reaches $2.0\ \text{m/s}$ in $4.0\ \text{s}$, so its acceleration is $a = (2.0 - 0)/4.0 = 0.5\ \text{m/s}^2$. As it slows to stop, the acceleration becomes negative even though the lift is still moving upward.

Example 2. A motorway journey. A car covers $90\ \text{km}$ in $1.0$ hour. Converting, $90\ \text{km} = 90000\ \text{m}$ and $1.0\ \text{h} = 3600\ \text{s}$, so the average speed is $90000 / 3600 = 25\ \text{m/s}$, which is about $90\ \text{km/h}$. Always convert before substituting.

Try this

Q1. State one scalar quantity and one vector quantity. [2 marks]

• Cue. Scalar: speed (or distance, mass, energy). Vector: velocity (or displacement, force, acceleration).

Q2. A train travels $4800\ \text{m}$ in $120\ \text{s}$. Calculate its average speed. [2 marks]

• Cue. $v = s/t = 4800/120 = 40\ \text{m/s}$.

Q3. A car slows uniformly from $30\ \text{m/s}$ to $12\ \text{m/s}$ in $6.0\ \text{s}$. Calculate its acceleration. [2 marks]

• Cue. $a = (12 - 30)/6.0 = -3.0\ \text{m/s}^2$ (a deceleration).