Motion
EQUATION
Average Speed
- Often, the speed of an object will change during a journey.
- Usain Bolt set the record for running 100M in 9.58 seconds. His speed would look like this:
Instead, we work out his average speed by doing the following: 
So it would be:
EXAMPLES
1. Car travelling 700m in 35s →
= 20m/s
2. Runner travelling 3m/s in 45 mins → 45 mins = 2700s 2700 2700s× 3 = 8100m
3. Runner travelling 2 m/s for 5km → 5km: 5000m, 
= 2500 seconds
Distance-time graphs
- Using a distance-time graph, we can represent how far an object travels from its start point.
Measuring Speed
- Average speed equations: 
- This means 
EXPERIMENT → To measure the final speed of a ball down a ramp
- Measure the time taken for the ball to go down the ramp.
- Repeat this and get the average. time. Then, change the height and repeat.
Height: 6 cm
Took an average time of 2.98s, therefore the average speed:
= 0.7m/s
Final speed is 
, therefore, the final speed = 0.8m/s
Height: 14 cm
Took average time of 1.61s, therefore the average speed:
= 0.7m/s.
Final speed = so the final speed = 1.4m/s.
Measuring instantaneous speed with light gates
- While the card interrupts the light beam, a timer runs inside the computer.
- The computer software calculates the speed of the car → you tell the computer how long the card is.
- It uses a formula: 
Velocity-time graphs
The gradient/slope of a line gives its acceleration on a velocity-time graph.
ACCELERATION → the rate of change of velocity
CALCULATING DISTANCE from a v-t graph
To find the distance, you work out the area under the line.
Calculating Acceleration
E.g., a car accelerates from 0 to 60 mph in 5s.This indicates that in order to calculate acceleration, we need to know the change in speed/velocity and time.
EXAMPLES
1. A car is changing its velocity from 0.5 m/s to 0.75 m/s; if this takes 0.1 s, then what's the car's acceleration at this time?
2. A car is travelling at 9 m/s and then accelerates with an acceleration of 12 m/s is the final velocity of the car 28 m/s, and how long did this acceleration take?
3. If a jet is travelling at 23 m/s and an acceleration of 7 m/s2 is applied for 12 s, what's the new velocity of the jet?
v = u + at 23 + (7 x 12) = 107 m/s
Motion Equations
The two equations of motion are:
If you haven't got the distance, use 
If you haven't got time, use v2 = u2 + 2as
EXAMPLE
A car accelerates at 4 m/s2 over 50 m. If it starts at 2 m/s, what speed does it reach?
We have SUVA, so we use v2 = u2 + 2as
v2 = 22 + (2 x 2 x 50)
v2 = 4 + 400 = 4 + 400
v2 = 404, so v = 
v = 20.1 m/s