3. Position & Motion
An object’s position is defined by a reference
point and a reference direction.
A reference point is something used for
comparison to determine if an object is in
An object is in motion If the object changes
position relative to a reference point.
4. Reference Point
Distance is the length of a path between two
Displacement is the length and direction an
object has moved from its starting point.
Don’t confuse distance with Displacement.
An object’s speed is the distance it travels in a
given amount of time.
Equation; Speed = distance/time
S = d/t
8. Practice problems...
Click for constant speed Word Problems...
9. Average speed Equation
In most real-world situations, speed is not constant but
changes, requiring several calculations.
Average speed = Total distance/Total time.
Average S = total d/total t
Sa = Dt /Tt
Dt = 32km + 13km = 45km
T t = 2hr + 1hr = 3hr
Sa = 45km/3hr, = 15km/hr
10. Instantaneous Speed
The speed at which an object is moving at a
particular point in time.
The slope of a d vs. t (d-t) graph is the rise over
the run (y over x). Active art Here
The slope of a d-t graph represents the speed.
13. Graphing speed, cont...
Reducing speeda Final speeda
14. More d-t graphs...
15. Which graphs are impossible?
A Vector is a quantity that has both a
magnitude and a direction. Example: 45
Velocity and speed are different!
Velocity is speed in a given direction.
IMPORTANT; Changes in velocity may be
due to change in speed, change in direction, or
18. Velocity equation
Velocity is change in speed or direction so...
Initial speed minus final speed...
V = S1 - S 2 = meters/sec = change in m/s.
If S1 - S2 is positive its speeding up.
If S1 - S2 is negative its slowing down.
A velocity always has a direction with it:
“3m/s in a N-W direction”
19. D-T graphs, slope, & velocity...
Change in speed or direction is called acceleration.
Increase in speed is acceleration, decrease in speed is
***An object can still be accelerating even if its speed
is constant if it changes direction. For example the
seats in a Ferris wheel are accelerating even though
the speed may be constant because they are moving in
21. Here’s what acceleration looks like...
22. Acceleration equation...
So... acceleration is change in velocity per unit of
time. Here’s the formula...
A = V1 - V 2 = meters/sec = m/s 2
T 1 - T2 sec
V1 is the initial velocity and V2 is the final.
23. Acceleration equation...
T1 - T2 is the total elapsed time...
T1 - T2 is always positive (can’t go back in time
if V1 - V2 is positive the object is accelerating
if V1 - V2 is negative the object is decelerating.
(note this is not how the book presents it...
24. Graphing Acceleration
If there is a curved line on a d-t graph the object
is either accelerating or decelerating.
Smile = accelerating
Frown = decelerating
25. This is acceleration on a d-t graph
Smile up = accelerating, smile down
26. This is acceleration
27. Graphing Acceleration on a v-t graph
A sloped line (either positive or negative) on a v-t
graph represents acceleration.
28. Equation for graphing acceleration on a V-T graph...
Only sloped portion is accelerating