1. Position and Displacement
Kinematics – Topic 1
Recap from Science 10

2. Scalars and Vectors
Scalar quantities: do not have a direction associated with them. They have magnitude (size) only.
Vector quantities: have magnitude AND direction. A vector will have an arrow above the symbol.
NOTE: Direction should be in square brackets. [N], [up], [West], etc. or use a + or - sign

3. Position Vector Symbol: d Position LOCATES an object.
Position has magnitude, direction, and origin.

4. Check Your Learning 1. Which of the following is a vector quantity?
A. 2.0kg
B. 34 km/h
C. 34 km/h [West]
D. 3.2s
C. It is the only answer with magnitude and direction.

5. Check Your Learning
2. Which of the following describes the position of an object?
A. 45 km
B. 45 km [E]
C. 45 km [East of the flagpole]
C – it is the only answer with magnitude, direction, and origin

6. Check Your Learning
3. A person leaves their house and walks 2.0km [East], takes a break, and then walks another 4.2 km [East]. What is their position?
Their position is 6.2 km [East] of their house.
Their displacement is 6.2 km [East].

7. Distance and Displacement
Distance (Δd) is a scalar quantity and refers to the total movement of an object without any regard to direction. An odometer in a car reads distance.
Formula: Δd = d1 + d2
Displacement (Δd) is a vector and refers to the change in position of an object.
Formula: Δd = df – di or Δd = d1 + d2

8. Example 1
A runner in a race is at a position of 43.2m to the right of the starting line when you first notice him. You turn your head briefly and then look back. He is now 82.6m to the right of the starting line. What was his displacement?

9. Answer Using formula: Δd = df - di Δd = 82.6 – 43.2 = 39.4m
The displacement is 39.4m to the right.
Drawing:

10. Example 2 A person walks 5.0km [East], and then 4.0km East].
A) Find Δd.
B) Find Δd.

11. Answer
Drawing:
A) This time there is no position but instead displacements given.
Δd = Δd1 + Δd2 =
= 9.0 km (no direction)
B) The displacement in this case is the same except it needs a direction.
9.0 km [East]

12. Example 3 A person walks 5.0km [E] and then 4.0km [W]. A) Find Δd.
B) Find Δd.

13. Answer Drawing: A) Δd = Δd1 + Δd2 = 5.0 + 4.0 = 9.0 km (no direction)
B) Δd = Δd1 + Δd2
= (-4.0)
= 1.0 km [E] or +1.0km

14. Check Your Learning
1. A person walks 850m [N], 320m [S], and then 130m [N].
A) What is her distance?
B) What is her displacement?
2. A runner completes a race by running around a 200. m circumference circular track 3 times.
A) What is his distance?
B) What is his displacement?

15. 1. A) 1300m
B) 660m [N] or +660m
2. A) 600m
B) 0m