1. Vector Calculations
A boat leaves a harbour and travels due north for a distance of 3km and then due west for a distance of 8km. What is the displacement of the boat with respect to the harbour?
A helicopter rise vertically from the ground for a distance of 600m and then moves horizontally for a distance of 1.6km. What is the displacement of the helicopter from its starting position?
‘Tough Guy’ Question
4. After take off an aircraft climbs at a rate of 150m/s at an angle of 30° to the ground. What are the magnitudes of the horizontal and vertical components of its velocity

2. Equations of motion

3. Starter
1. Put the following in order of average speed (slowest first) 2. Estimate the average speed for each of the above (in mph) 3. What is the difference between speed and velocity?

4. Starter (answers)
Average speeds: Snail = 0.03mph Car =70mph Cheetah = 70mph Tennis serve = 100mph Bullet = 1000mph Speed is a scalar quantity. Speed = distance ÷ time Velocity is a vector quantity. Velocity = displacement ÷ time

5. Learning Objectives s =(u + v) t 2 v2 = u2 + 2as s = ut + ½at2
Recognise that speed can change during a journey
Be able to calculate average speed
Be able to use the following equations:
v = u + at
s =(u + v) t 2
v2 = u2 + 2as
s = ut + ½at2

6. Success criteria
Use the equations of motion directly to find required values. (Grade C)
Rearrange the equations of motion to find required values (Grade A)

7. How do we calculate (average) speed?
Speed = distance
time
This basic equation means we can only
solve a limited amount of problems.

8. So we need something a little more complex...
Click for video
The Bugatti Veyron goes from 0-200mph (or 89m/s) in 24.2 seconds. How many metres does it travel in this time?
We can’t use speed=distance/time because the car was accelerating.

9. These are the 4 equations of motion you must be able to use:
v = u + at
s =(u + v)t 2
v2 = u2 + 2as
s = ut + ½at2
What does each letter mean?
Take care: all units of distance and time must match. If they don’t, you must convert them.

10. Back to the Bugatti question...
The Bugatti Veyron goes from 0-200mph (or 89ms-1) in 24.2 seconds. How many metres does it travel in this time?
Which equation should we use?
v = u + at
s =(u + v)t 2
v2 = u2 + 2as
s = ut + ½at2

11. Using s =(u + v)t 2 s = ? u = 0ms-1 v = 89ms-1 t = 24.2s
The Bugatti Veyron goes from 0-200mph (or 89ms-1) in 24.2 seconds. How many metres does it travel in this time?
Using s =(u + v)t
s = ?
u = 0ms-1
v = 89ms-1
t = 24.2s
s = (0 + 89)x24.2 2
s = m

12. Higher level
For the higher paper you will be expected to rearrange the equations of motion.
For example.....

13. Question: A skateboarder goes from standstill to 6m/s in 3 seconds
Question: A skateboarder goes from standstill to 6m/s in 3 seconds. What is her acceleration?
v = 6, u = 0, a = ?, t = 3 Using v = u + at 6 = 0 + (a x 3) 6 = 3a 6 = a 3 a = 2ms-2

14. Equations of motion
The best way to learn how to do these is practice!! Question sheet P5b5 - old course