IB physics - displacement

1. LECTURE 2
Displacement
Position vs time plots
IB Physics Power Points
Topic 2
Kinematics
www.pedagogics.ca

2. Displacement
Displacement is defined as the straight line path between an
object’s initial position and an object’s final position.
Displacement is a measurement of the change in position of a
moving object.
Displacement is not necessarily the distance travelled!
s = 7 km [E] (displacement)
s = 12 km (distance)

3. Displacement (continued)
Victor begins his walk 3 km [S] of Starbucks. 2 hours later,
he ends his walk at his friend’s house 2 km [N] of Starbucks.
What is Victor’s displacement?
- x direction
South
+x direction
NorthStarbucks
ref pt
We can see that Victor’s change in position equals
5 km [N]

4. Displacement (continued)
Mathematically, Victor’s displacement (Δs) can be calculated by :
Displacement = change in position = final position – initial position
- x direction
South
+x direction
NorthStarbucks
ref pt
Initial position
3 km [South]
Final position
2 km [North]
Δs = sfinal – sinitial = 2 km [N] – 3 km [S]
= 2 km [N] – -3 km [N]
= 5 km [N]
5 km [N]

5. Displacement (continued)
Starbucks
final position
Initial position
3 km [South]
House
2 km [North]
Δs = sfinal – sinitial = zero – 3 km [S]
= zero – -3 km [N]
= 3 km [N]
Victor picks up his friend and they take 1 hour to walk back
to Starbucks for a coffee. What is Victor’s displacement
relative to his starting point?

6. Displacement (continued)
-3
-2
-1
0
1
2
3
0 1 2 3 4
time (hrs)
Position[N]km
We can also show Victor’s walk on a position vs time graph
Start
Friend’s house
Starbucks
(reference pt.)

7. -3
-2
-1
0
1
2
3
0 1 2 3 4
time (hrs)
Position[N]km
How far did Victor walk?
Start
Friend’s house
Starbucks
5 km + 2 km = 7 km (DISTANCE)

8. -3
-2
-1
0
1
2
3
0 1 2 3 4
time (hrs)
Position[N]km
What is Victor’s change in position?
Start
Friend’s house
Starbucks
= 3 km [N] (DISPLACEMENT)

9. More about position vs time graphs
Biff walks down the hallway and travels a constant 1.5 m
[North] each second. What would a position vs time
graph look like?
0
2
4
6
8
10
0 1 2 3 4 5 6 7
time (s)
Position[N]m
Biff is changing
his position by 1.5
m [N] each second
he walks.

10. More about position vs time graphs
Biff’s average velocity is 1.5 ms-1 [N]. How is this value
related to the graph?
0
2
4
6
8
10
0 1 2 3 4 5 6 7
time (s)
Position[N]m
Δs = 9 m
Δt = 6 s




 -1
9 m
6 s
1.5 ms
s
slope
t

11. KEY CONCEPT: DON’T EVER FORGET THIS
The slope of line connecting any two points on a
position vs time graph represents the average
velocity (speed).
If the slope of a position vs time graph changes,
then the velocity MUST also be changing.

12. An example:
Determine the velocity for each segment of this position vs
time graph
/m [N]
s
/s
t
A = 3 ms-1[N]
B = 0 ms-1
C = -4 ms-1[N] or 4 ms-1[S]
D = 0 ms-1
E = 6 ms-1[N]
F = 0.9 ms-1[N]

13. What have we learned so far about position vs
time graphs?
Slope indicates velocity (speed)
A steeper slope indicates a greater velocity.
A slope of zero (horizontal) means object is not
moving (at rest).
Negative slopes mean the object is moving in the
opposite direction.

14. 0
100
200
300
400
500
600
0 5 10 15
t /s
s/m[downwards]
Now consider a graph of a falling ball (strobe analysis
lab): The graph is a curve. What does that mean?
The slope of the tangent line
represents the instantaneous
velocity at t = 5 s.
We can estimate the slope
at any point by drawing a
tangent to the curve.
Let’s draw a tangent at t
= 5 s

15. 0
100
200
300
400
500
600
0 5 10 15
t /s
s/m[downwards]By drawing two simple tangents, we can see that the slope of
the tangent line increases as the ball falls.
Slope represents
velocity and it makes
sense that a falling
ball speeds up!!!

16. 0
100
200
300
400
500
600
0 5 10 15
t /s
s/m[downwards]
Average velocity is defined as the overall displacement
divided by the time. The average velocity between any
two times would be the slope of a line connecting those
points.
The slope of this line
represents the average
velocity for the time
interval 0 to 10 s

17. Consider a trip downtown. You may drive on the
expressway, on local streets, and you will stop at red
lights. A trip might look like this.
Determine the
average speed for the
entire trip?
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30
time (min)
Position(km)
0.6 km/min