2.1 - Speed, Velocity & Displacement

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.

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.