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

2. Position vs Time Graph Δd Δt Slope = v = Δd/Δt v = (40 m)/(8 s)
Graph of a toy car
The slope of a position vs time graph equal to the objects velocity. Δd Δt
The line of this graph is straight which means the velocity of the object must be constant.
Slope =
v = Δd/Δt
v = (40 m)/(8 s)
v = 5.0 m/s
How would this constant velocity be shown on a Velocity vs Time graph?

3. Velocity vs Time Graph Graph of a toy car
The line is horizontal. Why is this?
What does a horizontal line on a velocity vs time graph mean?
What does the slope of a velocity vs time represent?
Answer:
The objects acceleration!
Since the object is travelling at a constant velocity of 5.0 m/s, it’s acceleration would be zero!
The slope of this line is also zero! The two ideas both agree with each other!

4. Position & Velocity vs Time Graph
Constant or Uniform velocity of 5.0 m/s
Both of these graph show the SAME motion.
They just show it in different ways because the graphs are different!

5. Position vs Time Graph Velocity vs Time Graph
A car travels at a constant speed while covering a distance of 20 m in 10.0 s. The car stops and waits 30 s for a traffic light to change. The car then travels another 50 m in 15.0 s before coming to a stop in front of a stop sign. After 5.0 s the cars turns around and heads back towards its original position at a constant speed, reaching this position in 10.0 s.
Graph this car’s motion on the Displacement vs Time graph given.

6. Position vs Time Graph Not moving at all
Moving quickly, rightward (+), constant velocity
Moving quickly, leftward(-), constant velocity
Moving slow, rightward (+), constant velocity

7. Velocity vs Time Graph
Draw a Velocity vs Time graph for the described earlier.

8. Position vs Time Graph Velocity vs Time Graph
Graph of a motion of a toy car
These two graphs show the exact same motion.
Although they look very different they give you the same information about the car’s position and speed at different times.
Slope = speed =2.0 m/s
Area under line = displacement = 20 m
Slope = acceleration = 0 m/s2

9. Position vs Time Graph Velocity vs Time Graph
How is constant velocity shown on a d vs t graph?
At an angle
How is constant velocity shown on a v vs t graph?
A straight horizontal line
What is the slope of d vs t graph represent?
The velocity
What is the slope of v vs t graph represent?
The Acceleration

10. Position vs Time Graph Velocity vs Time Graph
How do you get the speed of an object from a d vs t graph?
Analyzing the slope
How do you get the speed of an object from a v vs t graph?
Analyzing the straight lines
How do you get displacement from a d vs t graph?
Take two points and subtract df from di
How do you get displacement from a v vs t graph?
Take the area under the graph between two points

11. Position vs Time Graph Velocity vs Time Graph
Now try this:
You leave your home and slowly walk at a constant speed towards a mailbox to mail a letter. On the way to the mailbox you stop to talk to your friend. After a short time you run to the mailbox at a higher constant speed to beat the mail truck. You spend a short time at the mailbox mailing your letter. You begin to stroll home slowly when all of a sudden your are knocked down on the ground by your friendly neighbourhood St. Bernard dog. After a few seconds of being licked on the face you realize you are late for dinner and you run really fast all the way home.
Sketch a Distance vs Time graph of this motion and then sketch a Velocity vs Time graph of this motion.

12. Position vs Time Graph Velocity vs Time Graph
You leave your home and slowly walk at a constant speed towards a mailbox to mail a letter.
On the way to the mailbox you stop to talk to your friend.
After a short time you run to the mailbox at a higher constant speed to beat the mail truck.
You spend a short time at the mailbox mailing your letter.
You begin to stroll home slowly
When all of a sudden your are knocked down on the ground by your friendly neighbourhood St. Bernard dog.
After a few seconds of face licking you realize you are late for dinner and you really run all the way home. D v t 4 5 3 6 2 1 7 t 3 1 4 6 2 5 7

13. Displacement and Distance Velocity and Speed from Motion of Toy Car
1. Find the displacement from 60 to 70 seconds. Using the D vs T graph 𝐷 = df – di = 0m - 70m = -70 m Using the V vs T graph 𝐷 = Area under the Graph = (-7)(10) = -70 m
2. Find the distance from 60 to 70 seconds. Using the D vs T graph D = 70 m Using the V vs T Graph Distance cannot be found as the area under the graph tells us the displacement

14. 3. Find the Average Velocity between 60 – 70 seconds
Using a D vs T Graph 𝑉 = ∆𝑑 𝑡 = −70 𝑚 10 𝑠 = -7 m/s
Using a V vs T Graph Just examine the graph it will tell you. 𝑉 = -7 m/s
we can find the Average velocity using either a D vs T graph or a V vs T Graph.
Using a D vs T graph, Find the corresponding points on the graph, join them by a straight line and find the slope.
Using a V vs T Graph we would need to find the total displacement over time. You could have three sections to examine three different displacements that you need to record.

15. 4. Find the Average Velocity between 20 – 70 seconds
using a D vs T Graph Find the corresponding points on the graph, join them by a straight line and find the slope. Straight line from 20 seconds to 70 seconds has a rise of -20 and a run of 𝑉 = ∆𝑑 𝑡 = −20 𝑚 50 𝑠 = -.4 m/s
using the V vs T graph 𝐷 1 = Area under the V vs T Graph = (0)(20) = 0 m 𝐷 2 = Area under the V vs T Graph =( )(15) = 50 M 𝐷 3 = Area under the V vs T Graph = (-7)(10) = -70 m 𝐷 𝑇𝑜𝑡𝑎𝑙 = m – 70 m = -20 M 𝑉 = ∆𝑑 𝑡 = −20 𝑚 50 𝑠 = -.4 m/s

16. 5. Find the average speed between 20 – 70 seconds d = 50 + 70 = 120 m
V = 𝑑 𝑡 = 120 𝑚 10 𝑠 = 12 m/s

17. Assignment Work on the Handout
NOTE: For question #1 what you are observing is every 1 second as object is moving 2 m.