1. Relationships between Position vs Time and Velocity vs Time graphs
Part II

2. Position vs Time during Acceleration
Notice on a d vs t graph during acceleration it is a curve.

3. Position vs Time during Acceleration
Negative Velocity
(speeding up)
Negative Acceleration
Positive Velocity
(slowing down)
Negative Acceleration
Sad Face = Negative Acceleration
Negative Velocity
(slowing down)
Positive Acceleration
Positive Velocity
(speeding up)
Positive Acceleration
Happy Face = Positive Acceleration

4. Between t = 0 s and t = 2. 0 s the object moves 8
Between t = 0 s and t = 2.0 s the object moves 8.0 m and its average velocity for this time interval is 4.0 m/s. (vavg = 8.0m/2.0s)
Each point examined is the Average velocity.
Between t = 0 s and t = 4.0 s the object moves 32 m and its average velocity for this time interval is 8.0 m/s. (vavg = 32m/4.0s)
Different
average
velocities
depending
upon the
time
interval.

5. To Find Instantaneous velocity from the Position-Time graph
Construct a straight line that is tangent to the position-versus- time graph at the point or instant in question.
Calculate the slope of that line.

6. Velocity vs Time Positive vs Negative
Recall velocity is a vector, therefore the direction it is moving will tell us if it has a positive velocity or a negative velocity.
On a V vs T graph:
An object is moving in the positive direction if the line is located in the positive region of the graph (whether it is sloping up or sloping down).
An object is moving in the negative direction if the line is located in the negative region of the graph (whether it is sloping up or sloping down).
If a line crosses over the x-axis from the positive region to the negative region of the graph (or vice versa), then the object has changed directions.

7. Velocity vs Time Positive vs Negative

8. Velocity vs Time Speeding up vs Slowing down
Speeding up means that the magnitude (the numerical value) of the velocity is getting large. For instance, an object with a velocity changing from +3 m/s to + 9 m/s is speeding up. Similarly, an object with a velocity changing from -3 m/s to - 9 m/s is also speeding up.
In each case, the magnitude of the velocity (the number itself, not the sign or direction) is increasing; the speed is getting bigger.
The object is speeding up if the line is getting further away from the x-axis (the 0-velocity point); and conversely, if the line is approaching the x-axis, then the object is slowing down.

9. Velocity vs Time Speeding up vs Slowing down

10. Position vs Time Graph Velocity vs Time Graph
For d vs. t graphs:
Slope = rise = displacement = velocity
run time
Use a tangent line to find instantaneous velocity.
For v vs. t graph:
Slope = rise = velocity = acceleration
run time
Area under graph = velocity x time = displacement

11. Check your understanding

12. Answers
Time 1
Time 2
Time 3
Time 4
Time 5
Time 6
Time 7
Time 8
Position + −
Velocity
Acceleration
Acceleration/ Deceleration A D

13. Some fun practice

14. Draw some Graphs
1) A cycler is at a stop light. When the light turns green it accelerates forward at a constant rate. It then approaches a red light where it slows down at a constant rate and comes to a stop. The cyclist moved forward for 20 seconds, and took 10 seconds to slow down to a stop.
Sketch ‘d vs. t’, ‘v vs. t’ graphs of its motion from the start of the green light to the end at the red light.

15. Draw some Graphs
2) A racing car opens its parachute 30 metres from its stopping point. Upon opening its parachute, it slows down at a constant rate and comes to a stop within 40 seconds.
Sketch ‘d vs. t’, ‘v vs. t’ graphs of its motion from the moment it opens its parachute to the point where it comes to a stop.

16. Draw some Graphs
3) Imagine a car at a stop light. When the light turns green it accelerates forward for 30 metres. From 0 m – 5 m it’s velocity went from 0 m/s to 20 m/s. It remained at 20 m/s for another 20 metres, where it slowed down at a constant rate to a stop over the remaining distance.
Sketch ‘d vs. t’ and a ‘v vs. t’ graph of its motion from the start of the green light to the end of the next red light.

17. Draw some graphs
4) Johnny walks his dog 20 metres for 5 minutes at a constant velocity heading west. He then waits for 1 minute while his dog goes to the bathroom. He then turns around and walks at a constant velocity for 8 minutes heading east for 30 metres to meet with his friend. They stay there talking for 5 minutes, then Johnny heads back home at a constant velocity.
Sketch ‘d vs. t’ and a ‘v vs. t’ graph of its motion from the start of the green light to the end of the next red light.

18. Assignment
In the Workbook Work on the Position vs Time Graphs and the Velocity vs Time Graphs. Only do the Acceleration vs Time Graphs if you like.