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 |
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1. Calculate the velocities: |
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(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 |
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2. Calculate the distances travelled: |
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(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 |