Speed, velocity, scalars and vectors
Forces can change the position, shape or motion of an object. They can make objects speed up, slow down or change direction. It is the direction of movement that shows the difference between a A quantity that requires only a size, for example, distance travelled is 20 m. and a A measurement having size (magnitude) and direction, eg a displacement of 4 m North. measurement – this is the difference between the speed of an object and its velocity.
Speed
Speed is a measure of how fast something is travelling. It is the A length measured in centimeters (cm), metres (m) or kilometers (km), eg 4 m. travelled in unit time. Speed is measured in m/s or km/h (or mph in UK cars).
\(\text{speed}=\frac{\text{distance travelled}}{\text{time taken}}\)
Speed, or distance and time can be calculated using the DST triangle.
Cover the letter you want to find to get the formula you need.
- D = S × T
- S = D ÷ T
- T = D ÷ S
Question
If a car travels 24 m in 2 seconds, what is its speed?
Speed = distance travelled ÷ time
24 m ÷ 2 s = 12 m/s.
Velocity
The only difference between velocity and speed is that velocity has a direction.
\(\text{velocity}=\frac{\text{displacement}}{\text{time}}\)
Quantity describing the distance from the start of the journey to the end in a straight line with a described direction, eg 50 km due north of the original position. is the distance moved in a straight line, or a given direction from the starting point.
Question
If a car travels 24 m east in 3 seconds, what is its velocity?
Velocity = displacement ÷ time
24 m ÷ 3 s = 8 m/s east
Question
You walk all the way around the house in the diagram in 20 seconds.
a) What is your speed?
b) What is your velocity?
a) Your speed = D ÷ T = (10 m + 10 m + 10 m + 10 m) ÷ 20 s
= 40 m ÷ 20 s = 2 m/s
b) Your velocity is zero. This is because your displacement is nothing. You have ended up at your original position. No net distance in a straight line has been made between the start and end point.
Scalars and vectors
Measurements that have magnitude (size) only are called scalar measurements.
Measurements that have size and direction are called vector measurements.
Some scalar measurements you are likely to use in Physics are:
- distance
- speed
- time
Some vector measurements you are likely to use in Physics are:
- displacement
- velocity
- acceleration
- force
- momentum
Question
Find the distance travelled by a runner moving at 9 m/s for 4 seconds.
D = S × T
9 m/s × 4 s = 36 m
Question
Find the time taken to cover 256 m at a speed of 8 m/s.
T = D ÷ S
256 m ÷ 8 m/s = 32 s
Question
Find the velocity of a train if it covers 1,000 metres in a south direction in 25 seconds.
S = D ÷ T
1,000 m ÷ 25 s = 40 m/s south. Don’t forget the direction.