2.2 - Speed, Velocity & Displacement

Distance and displacement

• Distance is how far an object has moved. It's a scalar quantity - it has a size but no direction.
• Displacement is a vector quantity - it measures the distance and direction in a straight line from the start point to the finish point (e.g. 5 metres north).
• Direction can be given relative to a point (e.g. towards the school) or as a bearing - a three-digit angle measured clockwise from north (e.g. 035°).
• For the same journey, the two values can differ: walking 5 m north then 5 m south gives a distance of 10 m, but a displacement of 0 m because you finish where you started.

Speed and velocity

• Speed is the distance an object travels per unit time (how fast it is going). It's a scalar quantity with no direction.
• Velocity is the speed of an object in a given direction (e.g. 20 m/s at 060°). It's a vector quantity.

Constant speed, changing velocity

• Because velocity includes direction, an object can travel at a constant speed while its velocity changes by changing direction.
• An object moving in a circle at a constant speed has a constantly changing velocity because its direction is always changing (e.g. a car going round a roundabout).

Average speed

Objects rarely travel at a steady speed, so the value usually quoted is the average (mean) speed.

Scalar and vector quantities

• A scalar quantity has a size (magnitude) only (e.g. speed, distance, mass, energy, temperature, and time).
• A vector quantity has both a size and a direction (e.g. force, velocity, displacement, acceleration, weight, and momentum).

Drawing and signing vectors

• A vector is drawn as an arrow: the length shows the size of the quantity, and the way it points shows the direction.
• When working with vectors along a straight line, take one direction as positive and the opposite as negative.
  • Example: a car moving one way has a velocity of 3 m/s; moving the opposite way it has a velocity of -3 m/s. Its speed is 3 m/s in both cases.

Calculating speed from distance and time

For an object moving at a constant speed (or velocity):

Distance (or displacement) = speed (or velocity) × time

Average speed over a whole journey

When speed varies across a journey:

$$\text{Average speed}=\frac{\text{total distance travelled}}{\text{total time taken}}$$

To measure the speed of an object moving at constant speed: time how long it takes to travel a measured distance, then divide the distance by the time.

Worked example - Speed and time of a cat

A cat walks 25 m along a straight path in 50 s. Find its speed, then how long it would take to walk 100 m at that same speed.

Typical everyday speeds

Factors affecting everyday speeds

• How fast a person walks, runs, or cycles depends on their fitness, age, the distance travelled, and the terrain.
• The speed of sound in air is about 330 m/s (it varies in different materials).
• Wind speed varies from a few m/s up to gale force, and is affected by temperature, atmospheric pressure, and nearby structures.

Converting units in speed calculations

• Kilometres to metres - Multiply by 1,000 (e.g. 16 km = 16,000 m).
• Milliseconds to seconds - Divide by 1,000 (e.g. 22 ms = 0.022 s).
• Hours to seconds - Multiply by 3,600 (e.g. 8 hours = 8 × 3,600 = 28,800 s).
• mph to km/h - Multiply by 1.6 (e.g. 30 mph = 30 × 1.6 = 48 km/h).
• km/h to m/s - Divide by 3.6 (e.g. 48 km/h = 48 ÷ 3.6 = 13 m/s to 2 s.f.).