1. Dynamics and Space Learning Intention You will be able to:
Discuss and compare the difference between scalar and vector quantities.
Carry out calculations involving displacement and instantaneous and average velocity.
Calculate the resultant of two vector quantities in two dimensions.

2. Vectors and scalars
In physics there are two groups of measurable quantities.
One group has size and direction, this group is known as vectors.
The other group has only size, this group is known as scalars.

3. Distance and displacement
It is important that you know the common vector and scalar quantities. A B
18 km
12 km N
Distance and displacement
Distance is how far you have travelled, the winding route from A to B.
Displacement is the straight line distance from A to B. Direction is important, it must go from A to B. In this case the direction would be due east.
Speed and velocity
Speed is distance ÷ time
Velocity is displacement ÷ time
The direction of the velocity will be the same as the direction of the displacement.

4. Copy the table below.
You will add new quantities as they appear in the course.
scalars
vectors
distance
displacement
speed
velocity
time
force
energy
acceleration 
temperature
 mass

5. Example: It takes a runner 2 hours to run from A to B along the winding route.
Calculate their average speed and average velocity.
average speed = distance ÷ time
= 18 ÷ 2
= 9 km/h
average velocity= displacement ÷ time
= 12 ÷ 2
= 6 km/h due east.

6. 1 A man walks from X to Y along a winding road.
What is his displacement at the end
of his walk?
b) What distance has he walked?

7. 2 If the walker in question 17 took 40 minutes for his walk, what was
a) his average speed
b) his average velocity?

8. 3 One complete lap of a running track is 400m.
An athlete completes one lap in 48 s in the 400 m race. What is his
a) distance travelled
b) displacement
c) average speed
d) average velocity.

9. 4 Repeat Q 3 for a runner in the 800 m race whose winning time was 1 min 54 s.

10. More than one force
In most situations there will be more than one force acting on an object. If we want to calculate the acceleration of the object we must first find the unbalanced force. The combination of forces is known as the resultant.
Example: The engine of the car provides a driving force of newtons. The frictional force acting on the car is 1 00 newtons. The mass of the car is 800 kg. Calculate the unbalanced force.
2 500 N
100 N
800 kg
Find unbalanced force.
Fun = – 100
Fun = 2 400N

11. 5 A car travels 40 km north, then turns back south for 10 km
5 A car travels 40 km north, then turns back south for 10 km. The journey takes 1 hour.
What is
a) the displacement of the car
b) the distance the car has travelled
c) the average velocity of the car }use km h-1
d) the average speed of the car? } use km h-1

12. 6 What are the resultants of the following forces?

13. More than one force
Sometimes when more than one force acts on an object they are not in the same dimension [up – down, left – right]. This makes it more difficult to calculate the resultant force.
You will need to make use of some of your maths skills for this.

14. Example: Two forces act on a box as shown below.
Calculate the size and direction of the resultant force.
3 N
4 N
resultant
4 N
3 N θ
Resultant; Pythagoras r2 =
r2 =
r2 = 25
r = √25
r = 5 N.
This is only part of the answer. Next you need the direction.
Using Trigonometry tanθ = = = 1.33
θ = 53.1˚
Answer: resultant force is 5 N 53.1˚ above the horizontal.
Any direction given must be relative to a fixed direction, an angle on its own is not enough. Only a 3 figure bearing is ok on its own.

15. 7 By using a scale diagram or otherwise, find the resultant of the following pairs of forces.

16. 2006 I2 Q22.
A fully laden oil tanker of mass 7.5x108 kg leaves a loading terminal.
Its engine and propellers produce a forward force of 6.0x106 N.
A tugboat pushes against one side of the tanker as shown.
The tug applies a pushing force of 8.0x106 N.
(a) Using a scale diagram or otherwise, find the size of the resultant of these two forces.
(b) Calculate the initial acceleration of the tanker.