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 STRATEGIES1. 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 everything3. Identify what you are trying to solve.

a. Write down knowns and unknownsb. Find an Equation that includes these values (if needed)

4. Solve the problem5. 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!

EXAMPLES1. 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 direction2. Subtract displacements in opposite directions3. 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=• 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:

• 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=?• Equation:

• 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

• 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.

• Let’s derive the units:•Units for velocity=m/s units for time =s

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:

• 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• Equation: a• a• a• 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)• Equation: • a• 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?

• 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-bullet-235668