# Velocity and displacement

In Physics we have to be a little more exact when talking about speed - the DIRECTION that something moves is just as important as how FAST it moves.

Imagine two photographs taken of a football match, one at the start and one at the end of the game. The referee may look as though he has only moved a few metres but in fact he will have run many kilometres during the game.

Think about a car starting off at a set of traffic lights. Moving FORWARDS at 2m/s may have a very different effect from moving BACKWARDS at 2m/s.

We use two new words to take into account this DIRECTION; they are DISPLACEMENT and VELOCITY

DISPLACEMENT is the distance measured in a certain direction.
VELOCITY is the speed measured in a certain direction

Displacement is measured in the same units as distance and velocity has the same units as speed.
Displacement is given the symbol s and velocity the symbol v and time the symbol t. So the formula for constant velocity is:

Velocity (v) = displacement (s)/time (t)
or
Displacement (s) = vt

## Constant speed and constant velocity

It is important to realise that there is a difference between CONSTANT SPEED and CONSTANT VELOCITY. If a car is moving in a straight line at a constant speed then its velocity is also constant but if it turns a corner, still keeping its speed the same, its velocity will have changed because the direction in which it was moving has changed.

Example problems
1. A car travels 80m due east for 4s at a constant velocity:
(a) what is its velocity?
(b) how far would it have travelled in two minutes if it carried on at the same velocity?
(a) v =s/t = 80/4 = 20m/s due east
(b) s = vt = 20 x 120 = 2400m due east
(notice the use of seconds here)

2. A bee flies across a 35m wide hockey pitch in 5s. What is the velocity of the bee?
v = s/t = 35/5 = 7m/s

 PROBLEMS space 1. Calculate the velocities: space (a) a car travels 20 km in 40 min (b) a lorry moves 48 m in 6 s (c) a snail crawls 360 mm in one hour (d) a golf ball rolls 20m in 2.5s space space 2. Calculate the distances travelled: space (a) a girl runs at 7m/s for 8s (b) a ship sails at 12km/s for 4 hours (c) a billiard ball rolls at 3m/s for 2s (d) a rabbit runs at 7.5 m/s for 1.5 minutes