CHAPTER 2: MOTION
WHAT IS MOTION?
• Motion is a change in an object’s position relative to some reference point
CHANGE IN POSITION
• 2 Different terms
1. Distance
• How far (in meters) that something has moved
2. Displacement
• Distance PLUS direction
• Relative to starting point
PROBLEM-SOLVING STRATEGIES
1. Read the problem. All of it, all the way to the end.
2. Draw a picture. This will be critical for some problems!
a. Label everything
3. Identify what you are trying to solve.
a. Write down knowns and unknowns
b. Find an Equation that includes these values (if needed)
4. Solve the problem
5. Round to 1 decimal place, unless otherwise noted.
6. Put answers in scientific notation if they are more than 3 digits.
7. Make sure to include units!
EXAMPLES
1. The woman ran 5 meters north, 2 meters east, 5 meters south, and then 2
meters west.
a) What was her distance traveled?
b) What was her displacement?
TO SOLVE PROBLEM
• We read the problem.
• Let’s draw a picture.
• Identify what we are trying to solve
• Distance-how far she’s moved
• Displacement-how far relative to starting
• No equation needed
• Solve problem
• Distance:5m+2m+5m+2m=14m
• Displacement=?
ADDING DISPLACEMENTS
• Rules:
1. Add displacements in the same direction
2. Subtract displacements in opposite directions
3. Displacements that are not in the same or opposite directions cannot be
directly added together.
BACK TO OUR PROBLEM
• 5m North-5m South=0m
• 2m East-2m West=0m
• Total: 0m+0m=0m
GUIDED PRACTICE
• To get to school from his house, Bobby walks 2 meters south and 3 meters
west. What is his distance traveled? What is his displacement?
DISTANCE
DISPLACEMENT
• The displacements don’t add and subtract nicely here, so how do we solve
it?
• Pythagorean Theorem
•
•
•
•
•
•
a2+b2=c2
22+32=c2
4+9=c2
13=c2
c= 13
C=3.6
YOU TRY IT
• To get to school, you leave your house and walk 4m east and 4m south.
• What is your distance from home?
• What is your displacement?
• Distance=10m
• Displacement=5.7m
SPEED
• The distance that an object travels in a certain amount of time.
• 60mph
• Traveling 60 miles in 1 hour
• Equation:
• 𝑠=
𝑑
𝑡
• Where s is speed, d is distance, and t is time
• The SI unit is m/s or km/hr
EXAMPLE PROBLEM
• A car traveling at a constant speed covers a distance of
750 meters in 25 seconds. What is the car’s speed?
• Picture not as useful in this case.
• Knowns: d=750m, t=25s
unknown: s=?
𝑑
• Equation: 𝑠 =
•𝑠=
750𝑚
25𝑠
𝑡
• s= 30m/s
• This is about highway speed.
GUIDED PRACTICE
• If the speed on a highway is 30m/s and a car travels 100 meters in 3 seconds,
are they speeding?
•
•
•
•
•
•
K: d=100m, t=3s
U:s=?
E:s=d/t
Solve: s=100m/3s
S=33.3m/s
They are speeding
YOU TRY IT
• How far does a car travel in 2 hours if it is moving at a constant speed of
20m/s?
• 40 km
TRIANGLE METHOD-NOT IN YOUR
NOTES
• When you are given an equation where there is a fraction on one side and a
single variable on the other, you can make them into a triangle.
• S=d/t
• Cover the variable that you are looking for, and your equation will be
revealed.
• d=st
• You should still know the algebra, but can use this trick if helpful
CONSTANT SPEED VS CHANGING
SPEED
• Constant speed: neither slowing down nor speeding up
• Changing speed: slowing down and speeding up
• We cannot solve this, so we need something else:
• Average speed: total distance and total time
• This is what we are solving.
• Instantaneous speed: The speed at a certain time (when you look at your
speedometer)
GRAPHING MOTION
• Distance vs. time graph
• Independent variable=time
• Dependent variable=distance
• The slope of the line is the speed
VELOCITY
• Velocity is related to speed, but they are not the same thing.
• Speed is a scalar (number only)
• Velocity is a vector (number AND a direction)
• Velocity-speed of an object and the direction of its motion.
• Same equation, only with a v instead of an s
• 𝑣=
𝑑
𝑡
• Same units (m/s)
VELOCITY VS. SPEED
• You can be traveling at the same speed, but have a different velocity.
• Traveling around a curve at a constant speed-speed is constant, but velocity
changes as the direction changes.
• Escalators
RELATIVE MOTION
• The choice of reference point affects how you describe motion
• See pg 53
MOMENTUM
• The product of an object’s mass and velocity
• Represented by letter “p”
• p=mv
• Let’s derive the units…
•
•
•
•
p=mv
Units for m=kg
Units for v=m/s
p=kg*(m/s)
• Always has a number and a direction
EXAMPLE PROBLEM
• A 90 kg running back is moving up the field (north) with a
velocity of 10 m/s. What is his momentum?
• Knowns: mass (90kg) velocity (10.0 m/s north)
• Looking for: momentum (p)
• Equation: p=mv
• P=(90kg)*(10.0m/s north)
• =900kg*m/s north
GUIDED PRACTICE
• A 40 kg student walks 10 meters in 5 seconds. What is her
momentum?
• Known: mass (40kg), distance (10m), time (5 sec)
• Unknown: momentum
• Equation: p=mv
• We don’t have the velocity! But we know how to get it…
• V=d/t
• =10m/5sec=2m/s
• P=(40kg)*(2m/s)
• =80kg*m/s forward
YOU TRY IT!
• An asteroid with mass 3*108 kg is heading for Earth with a velocity of 3*104 m/s.
When it hits Earth, what is its momentum?
• 9-1012kg*m/s towards Earth
COMPARING MOMENTUMS
• Which has more momentum: a car traveling 30m/s or a semi traveling
30m/s? Why?
• P=mv
• The velocities are the same, but the mass of the semi will give it more
momentum.
ACCELERATION
• The rate of change of velocity.
• Because velocity includes a direction, acceleration can be a change in
direction OR velocity.
• Acceleration can be positive, negative, or zero.
• When an object speeds up, the acceleration is POSITIVE
• When an object slows down, the acceleration is NEGATIVE
• When there is no change in velocity, the acceleration is ZERO
IN DISTANCE V. TIME GRAPH, THE
SLOPE IS THE ACCELERATION.
CALCULATING ACCELERATION
• Acceleration is change in velocity over time.
•𝑎 =
𝑣𝑓 −𝑣𝑖
𝑡
• Let’s derive the units:
• Units for velocity=m/s
•𝑎 =
𝑣𝑓 −𝑣𝑖
𝑡
=
𝑚 𝑚
−
𝑠 𝑠
𝑠
=
m
𝑠
s
units for time =s
=
m
s∗s
=
m
𝑠2
DELTA-NOT IN YOUR NOTES
• To represent change in a value, you can use the Greek letter delta (Δ)
• The equation for acceleration then becomes:
• 𝑎=
Δ𝑣
𝑡
• Where Δv is the change in velocity.
• This is useful for problems that only give you a change in velocity, not a
starting and ending velocity.
EXAMPLE PROBLEM
• A skateboarder has an initial velocity of 3m/s west, and
comes to a stop in 2 seconds. What is her acceleration?
• Knowns: Initial velocity (3m/s) final velocity (0m/s) and
time (2 seconds)
Unknown: a
𝑣𝑓 −𝑣𝑖
• Equation: a=
• a=
• a=
0𝑚 3𝑚
− 𝑠
𝑠
𝑡
2𝑠𝑒𝑐𝑜𝑛𝑑𝑠
𝑚
3𝑠
2𝑠𝑒𝑐𝑜𝑛𝑑𝑠
• a= -1.5m/s2 forward or 1.5 m/s2 backwards
GUIDED PRACTICE
• A vehicle begins at rest and reaches a speed of 30m/s in 5 seconds. What is
the vehicles acceleration?
• Knowns: Initial speed (0m/s) final speed (30m/s)
time (5 sec)
𝑣𝑓 −𝑣𝑖
• Equation: 𝑎 =
• a=
30𝑚 0𝑚
−
𝑠
𝑠
5 𝑠𝑒𝑐
=
30𝑚
𝑠
5 𝑠𝑒𝑐
𝑡
• a=6m/s2 forward
YOU TRY IT
• A vehicle is going through a town at a constant speed. As they leave town,
they increase speed by 21 m/s in 7 seconds. What is their acceleration?
• 𝑎=
Δ𝑣
𝑡
=
21 𝑚/𝑠
7𝑠
= 3𝑚/𝑠 2 forward
MOTION IN 2 DIMENSIONS
• Circular motion:
• When an object is moving in a circular path, the speed remains
constant but it is accelerating because of the motion changes
• Velocity is perpendicular to the inward acceleration.
• This “center seeking” acceleration is called centripetal acceleration
• Ex. Carousel
PROJECTILE MOTION
• When you throw an object, gravity pulls it downward.
• It follows a curved path
THROWING AND DROPPING
• Will a bullet dropped or a bullet fired hit the ground first?
• http://www.teachertube.com/video/myth-busters-dropped-vs-fired-bullet235668