1. Unit 1 Our Dynamic Universe Velocity-Time Graphs
CfE Higher Physics
Unit 1
Our Dynamic Universe
Velocity-Time Graphs

2. Learning Intentions Can I interpret velocity–time graphs including:
a) area under graph is displacement
b) gradient is acceleration
c) objects in freefall taking into account air resistance and changing surface area.
d) change a v-t graph into an a-t graph.

3. Velocity-time graphs From N5, you will already know the following:
The area under these graphs will be the displacement of the object.
The acceleration of the object can be found by finding the gradient of the lines.

4. Velocity-Time Graphs velocity time OA - constant acceleration AB -
constant velocity
BC -
constant deceleration
acceleration =
gradient of graph
displacement travelled =
area under graph

5. Velocity-time graphs
As we have previously learned, the direction of the object will tell us if it has a positive or negative value.
Remember that UPWARDS is positive and DOWNWARDS is negative.
Gravity always acts down.
The following graph will show these.

6. Velocity-Time Graphs – directionsB C O F E D - +
Positive direction
Negative direction
OA -
constant acceleration
CD -
constant acceleration
AB -
constant velocity
DE -
constant velocity
BC -
constant deceleration
EF -
constant deceleration

7. Velocity-time graphs for objects travelling vertically
When a ball is thrown up vertically, we take the following vectors as positive:
Displacement
Velocity
The acceleration due to gravity still acts downwards.
What would you expect the graph to look like?

8. Ball Thrown upwards

9. Ball Thrown upwards and coming back down
At the highest point, you can see that the final speed is 0 m/s

10. Ball thrown up, comes down and hits the ground.
Always split the journey into UP and DOWN.
As it travels downwards, the final speed now becomes the initial speed. i.e. u = 0 m/s

11. Some reminders
For all of these examples, air resistance is negligible.
Acceleration due to gravity is – 9.8 m s-2
At the highest height of travel, the final velocity is ZERO m/s.
Velocity and Displacement are positive upwards
Velocity and Displacement are negative downwards

12. The bouncing Ball
For an object that is dropped and bounces, what would you expect the velocity- time graph to look like?

13. Acceleration-time graphs
What would the following velocity – time graph look like as an acceleration – time graph?

15. v-t Graphs into a-t graphs
velocity
time A B C O F E D - +
acceleration
time O - + F A B C D E

16. Acceleration-Time Graphs+ F A B C D E

17. Success Criteria I can interpret velocity–time graphs including:
a) area under graph is displacement
b) gradient is acceleration
c) objects in freefall taking into account air resistance and changing surface area.
d) change a v-t graph into an a-t graph.