Physics of Motion:
Displacement, speed, velocity, acceleration and
momentum
We will be considering two kinds
of values/quanities…
• 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
5 mph N
Example: velocity (5 mph north)
What is motion?
• Change (Δ) in object’s position relative to a
reference point
Distance travelled
• Scalar quantity
• SI unit: meters (m)
• Path of object is important in measuring distance
travelled
Displacement
• Vector quantity
• Length and direction of change in object’s position
• Consider starting point and ending point, but not
HOW it got there
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)
Speed
• 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
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
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?
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)
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?
Calculating relative velocity
Object A
Object B
B’s velocity relative to A
10 m/s W – 5 m/s W =
5 m/s West
10 m/s West
5 m/s W
5 m/s W – 10 m/s W =
10 m/s West
5 m/s West
-5 m/s W =
5 m/s E
5 m/s West
10 m/s East
10 m/s E – (-5 m/s E) =
15 m/s E
10 m/s W – (-5 m/s W) =
5 m/s East
10 m/s West
15 m/s W
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?
Velocity does not translate to fun
Acceleration does!
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
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?
Experiencing a constant speed but
changing velocity
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
v = 2 m/s W
a = 0.4 m/s2 S
a = 0.4 m/s2 N
v = 2 m/s E
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
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.
Momentum Practice
• Which has more momentum (magnitude)? A high
school football linebacker sprinting at you 10.0
miles per hour, or a rubber band launched at you at
10.0 miles per hour?
• Which has more momentum? A baseball thrown at
15.0 m/s away from you, or a baseball thrown 30.0
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?