1. Velocity-Time Graphs and Acceleration

2. What does a v-t graph look like?
Time is marked on the horizontal axis and velocity is on the vertical.
Graphs that represent an object’s velocity versus its time.

3. What can we determine from a velocity time graph?
Velocity and speed
Time
Acceleration
Displacement and distance

4. What can we determine from a velocity time graph?
Velocity - reading directly off the y-axis
v(1.0) =
v(5.0) =
V(11.0) =

5. What can we determine from a velocity time graph?
Time (read off the x-axis)
Time when v = 50
b) Time when v = - 40
Time when v = 0

6. What can you find from a v-t graph
Instantaneous Acceleration = slope at a point on the graph (you may have to use a tangent)
Average acceleration = finding the slope of a segment (use the start and end points)

7. What can we determine from a velocity time graph?
Acceleration = v/t = slope
a(3.0)
b) a (4.0)
a (12.0)
a (ave for first 11.0 s)

8. What can we determine from a velocity time graph?
Displacement = area under the curve
NOTE: Area formulas:
Arearectangle = length x width
Areatriangle = ½ base x height
d (first 1.0s)
b) d (first 4.0 s)
a (entire trip)

9. Velocity-Time Graphs

10. Interpreting v-t graphs
Horizontal lines show uniform motion (constant speed and direction).
Inclined lines show change in speed or direction, or both: in other words accelerated motion.

11. Summary Slide: Velocity-Time Graphs
Independent Variable =
Dependent Variable =
Above x-axis =
Below x-axis =
On x-axis =
Linear sections

12. Summary Slide: Velocity-Time Graphs
Slope =
+ slope (2 scenarios)=
- slope (2 scenarios) =
Horizontal Line
Average acceleration:
Instantaneous acceleration:

13. Summary Slide: Velocity-Time Graphs
Steeper slope means _______________________
To find velocity: read off ______ at a point
To find displacement:
Find time: read off the at a point

14. Summary Slide: Velocity-Time Graphs
Independent Variable = time
Dependent Variable = velocity
Above x-axis = moving forward (positive v)
Below x-axis = moving backward (negative v)
On x-axis = stationary (v = 0)
Linear sections = constant acceleration

15. Summary Slide: Velocity-Time Graphs
Slope = acceleration
+ slope (2 scenarios)= moving forward, speeding up
OR moving backward, slowing down
- slope (2 scenarios) = moving forward, slowing down
OR moving backward, speeding up
Horizontal Line = no acceleration (slope = 0)
Average acceleration: draw a line from start to end and find its slope
Instantaneous acceleration: slope at a point (use tangent)

16. Summary Slide: Velocity-Time Graphs
Steeper slope means speeding up or slowing down quickly (changing speed quickly – like hitting the brakes rather than putting the brakes on 10m before stop sign)
To find velocity: read off y-axis at a point
To find displacement: area between curve and x-axis (find total area of rectangles and triangles)
Find time: read off the x-axis at a point