1. Quick Quiz
Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true):
moving in the positive direction.
moving with a constant velocity.
moving with a negative velocity.
slowing down.
changing directions.
speeding up.
moving with a positive acceleration.
moving with a constant acceleration.

2. Quick Quiz
Calculate the speed of the object during all 3 motion segments depicted in the graph.

3. recall speed  how fast an object is moving
average speed  the average of all instantaneous speeds; found by the distance/time ratio
instantaneous speed  the speed at any given instant in time

4. instantaneous speed
for uniform motion, the instantaneous velocity at any point will be the same as the average velocity across all points
for non-uniform motion (acceleration) these values will not necessarily be equal

5. instantaneous speed on a non-uniform motion graph
moving along the acceleration curve, the slope progressively increases (as speed increases)
to determine instantaneous velocity we must calculate the slope of the
tangent of the line on the
p-t graph
a tangent is a straight line
that contacts a curve at a
single point

6. Calculations and Graphs
Acceleration
Calculations and Graphs

7. acceleration
describes how quickly an object’s velocity changes over time (rate of change in velocity)
a vector quantity (directional)
average acceleration is given by the equation:
aav = Δv = vf – vi
Δt tf - ti
the standard unit for acceleration is m/s2

8. constant acceleration
when an object changes its velocity by the same amount each second
note: this is non-uniform motion since the speed is changing

9. direction depends on: Rule of Thumb:
if the object is speeding up or slowing down
if the object is moving in a + or – direction
Rule of Thumb:
if an object is slowing down, then its acceleration is in the opposite direction of its motion
if an object is speeding up, then its acceleration is in the same direction as its motion

10. In Example A, the object is moving in the positive direction (i. e
In Example A, the object is moving in the positive direction (i.e., has a positive velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration.

11. In Example B, the object is moving in the negative direction (i. e
In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down. According to our RULE OF THUMB, when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object also has a positive acceleration.

12. important note on direction
in physics, + and – signs have a physical meaning
they indicate direction
-2m/s2 represents acceleration in a negative direction, it does not mean the acceleration value is less than 0!

13. determining acceleration from graphs
Time Velocity (s) (m/s)

14. determining acceleration from graphs
Time Velocity (s) (m/s)