1. Displacement, speed, velocity, acceleration and momentum
Physics of Motion:
Displacement, speed, velocity, acceleration and momentum

2. We will be considering two kinds of values/quantities…
Scalars:
Quantities with only a magnitude
Examples:
Your height, your weight, the distance from the earth to the sun, your instantaneous speed in a car
Vectors
Quantities with both magnitude and a direction
Represented by a point with an arrow emanating from it
Length of arrow represents magnitude
Direction arrow is pointing represents direction
Example: velocity (5 mph north)
5 mph N

3. What is motion?
Change (Δ) in object’s position over time relative to a reference point

4. Distance travelled Scalar quantity SI unit: meters (m)
Path of object is important in measuring distance travelled

5. Displacement Vector quantity
Length and direction of change in object’s position
Consider starting point and ending point, but not HOW it got there

6. Example: baseball runner
A girl hits a baseball while at bat, and runs to first base, then runs 20 feet toward second base, and turns around and runs back to first base, where she is safe. Assuming second base is due north of home plate, what is a) the distance traveled by the runner, and b) the displacement of the runner?
(A baseball diamond has sides of 90 feet)

8. Speed Speed Average speed Scalar quantity
Distance traveled per (divided by) period of time
s = d/t
SI units: m/s
Average speed
s = d/t, where d is total distance and t is total time.
Path of travel must be considered, NOT displacement

9. Speed Instantaneous speed
The speed of an object at any given moment of time
For a car, what the speedometer reads
May be less than or greater than the average speed at any given time.
time

10. Speed Practice: driving to school Total distance = 3.0 miles
Total time = 8.25 minutes
What is the average speed in miles per hour (mph)?
During what circumstances would the instantaneous speed be:
less than the average speed?
More than the average speed?

11. Velocity Vector quantity: magnitude and direction
The magnitude of a velocity is a speed
v = d/t in a given direction
Example: 2 cars, one moving northbound on a highway, the other moving southbound, both with speeds of 25 m/s
v1 = 25 m/s north (+ 25 mph)
v2 = 25 m/s south (- 25 mph)

12. Relative motion For objects moving along the same line…
Subtract the velocity of the reference point from the velocity of the second object
Negative velocities in one direction are equivalent to the same velocity in the opposite direction
Think: are the objects moving farther apart or closer together?

13. Calculating relative velocity
B’s velocity relative to A
10 m/s W – 5 m/s W =
5 m/s W
5 m/s W – 10 m/s W =
-5 m/s W =
5 m/s E
10 m/s E – (-5 m/s E) =
15 m/s E
10 m/s W – (-5 m/s W) =
15 m/s W
Object A
Object B
5 m/s West
10 m/s West
10 m/s West
5 m/s West
5 m/s West
10 m/s East
5 m/s East
10 m/s West

14. Practice problem
A family flees Northwest in a car traveling 30.0 mph from a hurricane traveling toward them, northwest at 20.0 mph. How fast is the hurricane moving from the point of view of the family in the car? Assuming the velocities of the hurricane and car do not change, how long will it take for the family put 100 miles between them and the hurricane?

15. Velocity does not translate to fun
Acceleration does!

16. Acceleration Change in velocity per time 𝑎= ∆𝑣 𝑡 = 𝑣𝑓−𝑣𝑖 𝑡
Vector quantity—direction matters!
Two examples:
Changing speed
Changing direction
Positive acceleration means speeding up
Negative acceleration means slowing down
Zero acceleration means no change in velocity

17. Calculating acceleration example
Initially, a car is travelling 30. m/s southbound. 5.0 seconds later, it is travelling 15 m/s southbound. What is its acceleration? Has the car sped up or slowed down?

18. Experiencing a constant speed but changing velocity

19. Acceleration—changing direction
Because velocity is a vector with a direction, changing direction of movement is acceleration
Examples: carousel ride or taking a turn at a constant speed
Turning at a constant speed, an object’s…
Velocity constantly changes.
Is therefore accelerating toward the center of the turn (centripetal acceleration)
The acceleration is also constantly changing in direction but not magnitude
v = 2 m/s E
a = 0.4 m/s2 S
v = 2 m/s W
a = 0.4 m/s2 N

20. Momentum (p)
Related to how difficult it is to stop a moving object or get a resting object to move
p = mv
Vector quantity
Units: kg·m/s
The more massive and the faster an object is, the more momentum it has.

21. Momentum Practice
Which has more momentum (magnitude)? A high school football linebacker sprinting at you miles per hour, or a rubber band launched at you at miles per hour?
Which has more momentum? A baseball thrown at m/s away from you, or a baseball thrown m/s away from you?
If the baseball has a mass of 145 grams, what is its momentum if it is thrown 30.0 m/s south?