Distance and Displacement

1. POSITION, DISTANCE, &
DISPLACEMENT
AVERAGE SPEED AND VELOCITY
INSTANTANEOUS VELOCITY
Lecture for 9/18/07

2. Position, Distance, and
Displacement
 Set up a coordinate system
 Right is usually positive, left is usually negative
 Distance = total length of travel
 Displacement = change in position = final position –
initial position or ∆x = xf - xi
 Displacement can be positive, negative, or zero

3. Position, Distance, and Displacement Cont.
 What is your distance traveled if you start at your friend’s
house travel to the grocery store then back to your house?
 What is your displacement for the same route?
 What are some routes that you could take to have a negative
displacement?
 How about a displacement of zero?

4. Average Speed and Velocity
 Average speed = distance/elapsed time

5. Average Speed and Velocity Con’t.
 Average velocity = displacement/elapsed time
 Sign tells the direction of the object motion
 + sign means xf > xi
 – sign means xf < xi

6. Graphical Interpretation of Average Velocity
 Slope of a line connecting two points on an displacement vs.
time plot is equal to the average velocity during that time
interval
 Complete 1-8 on Creating velocity versus time graphs WS

7. Instantaneous Velocity
 Average velocity isn’t very descriptive about the exact
rate of motion of an object at a specific time
 Ideally you would calculate the average velocity for
every minute or second
 Instantaneous velocity, v =
 When the velocity is constant, average velocity over any
time interval = instantaneous velocity at any time
 When the velocity changes, the instantaneous velocity at
a given time is equal to the slope of the tangent line at
that point on a displacement vs. time graph