1. Quick Quiz
Consider a football coach pacing back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D. What is the coach's average speed and average velocity?

2. Representing Motion Using Graphs
Position-Time Graphs
Velocity-Time Graphs

3. position-time graphs
a graph describing the motion of an object, with position on the vertical axis and time on the horizontal axis
it is important to understand how the shape of a p-t graph relates to the motion it describes

4. straight line  the object is covering an equal distance per time interval (constant motion)
curved line  the distance covered each time interval is not consistent (non-uniform motion)

5. flat line  no change in position over time (standing still)
steep line  large change in position over time (moving quickly)
shallow line  small change in position over time (moving slowly)

6. negative/downward line  the object is travelling in a negative direction
can be uniform or non-uniform
can be fast or slow
*Therefore, by looking at a position- time graph, one can determine:
the direction of movement
the speed of the movement (slow or fast)
if the movement is uniform (constant speed) or non-uniform (acceleration)

7. slope slope is the measure of the steepness of a line
slope = rise = Δd = d2 - d1
run Δt t2 – t1
the slope of a p-t graph yields the velocity of the object
the steeper the line, the greater the velocity (increased displacement in a given amount of time)
if the line remains level, then velocity is constant

8. example examine the graph choose 2 points on the line (x, y)
apply the formula:

9. velocity-time graphs
a graph describing the motion of an object, with velocity on the vertical axis and time on the horizontal axis
useful when studying objects moving with constant velocity or constant acceleration
positive velocity positive velocity
zero acceleration positive acceleration

10. shape of v-t graphs show direction:
show change in velocity (acceleration)

11. comparing p-t and v-t graphs
the following motion yields:
position-time graph velocity-time graph
CONSTANT VELOCITY (UNIFORM MOTION)

12. comparing p-t and v-t graphs
the following motion yields:
position-time graph velocity-time graph
CHANGING VELOCITY (NON-UNIFORM MOTION)

13. area of a v-t graph
for a velocity-time graph, the area bound by the line and the axes represents the displacement of the object

14. equations for area calculations
recall the equations for calculating the area of basic geometric shapes
note that the area of a trapezoid can be calculated by finding the sum of the areas of the contained rectangle and triangle

15. practice
A = 30 m/s X 4 s A = 30 m/s X 3 s = 120 m = 90 m

16. practice
A = ½ X 1 s X 10 m/s A = ½ X 3 s X 30 m/s
= 5 m = 45 m

17. practice
A = ½ x 1s x (20+30 m/s) A = ½ x 2s x (30+10)
= 25 m = 40 m

18. 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.