Motion

What is motion?• A change in position

• What is Zach’s speed relative to Ed’s?• What is everyone’s speed relative to the cactus on

the side of the road?

Distance and Displacement

• Distance is the total length of a path traveled.• Displacement is the shortest distance between

two points– Doesn’t matter how you get there, as long as you

get there.– “as the crow flies”

VS.

Lombard St., San Francisco

• Which one is longer – distance or displacement?• Which one would you use to figure

out how much gas you’d need to get up/down the hill?• Which one would you use to find out

how far you got from where you started?

Speed

• When you’re in a car, how do you describe your speed? • Relative to what?

• What do those units mean?• Speed is the distance traveled, and the time taken to travel it.• Speed = (distance)/(time)

Velocity

• What is velocity?– Velocity is both SPEED and DIRECTION of travel.

• You might say “30 miles per hour North” or “50 m/s straight up”

• Velocity tells us not only the speed an object is going, but which direction it’s going in.

What is the velocity of the object?

• A pumpkin launched from a catapult, traveling 40 mph east

• A leaf blowing in the wind FROM the north at 3 meters per second (m/s)

• A dog that runs across a 30-yard stretch of field in 3 seconds

• A paintball that splatters after flying 5 m/s at your friend

• A bird that migrates down across the country (about 1,582 miles) to Central America in 2 weeks

Velocity and graphs• What is happening in this graph?

Does this graph tell a story?

Acceleration

• Acceleration is a change in velocity– Speed OR direction

• Acceleration tells us that velocity is changing– Like when you step on the gas pedal in a car, the

car speeds up– …or when you step on the brake, the car slows

down– …OR when you turn the wheel, the car changes

direction. THIS IS ACCELERATION AS WELL!

• Acceleration has units that tell us what our change in velocity (m/s) is per time (s)– Acceleration = velocity/time– The units look like this: (m/s)/s = m/s2

• Acceleration can be a positive or negative number– This positive or negative tells us which direction we’re

headed.– Positive means we’re headed in the same direction we

started in (speeding up)– Negative means we’re starting to move in the opposite

direction we started in (slowing down/reversing)

What does this acceleration tell us?

• If my car is headed north at 50 mph and I start to accelerate, what is my velocity in ONE HOUR if my acceleration is:• 10 mph• 20 mph• 30 mph• -10 mph• -20 mph

Tell me a story

First, Let me point out some things

This flat line indicates a time of CONSTANT VELOCITY – no changing speed or direction

Negative velocity means we’re headed backwards!

Positive slope means we

are speeding up

Final velocity is 0 m/min, so we have stopped (makes sense, right?)

For a REAL challenge…

What would this graph look like as “distance vs. time?”

Practice problems

• If you leave your house and travel 5 miles North, 3 miles East, 2 miles West, 2 miles North, and 1 mile West (consider drawing a diagram) to reach school, then:– What is your DISTANCE?– What is your DISPLACEMENT?– If it took you 19.5 minutes to travel that distance,

what was your SPEED?

• Climbing a tree is hard work, but koalas manage it. If a koala climbed up a 50-foot tree in 2 minutes, then:– What is his distance?– What is his displacement?– What is his VELOCITY?

• After flinging a clay pigeon into the air, a shooter has to guess the path of the target if they want to aim appropriately. The pigeon (a round, painted disk) flies across the 40-yard field with a speed of 10 yards/s.– How long does the shooter have to hit the target?– What is the pigeon’s velocity?– If gravity wasn’t a factor, how far would the pigeon

go in 1 minute?

• At the intersection of Fairview and Morgantown, there is a roundabout. If the circumference of the roundabout is 50 yards, find the distance and displacement for:– 1 lap around– 2 laps around– 3 laps around– Can you have a constant speed on a roundabout?– Can you have a constant velocity?

• A penny dropped from the Empire State Building won’t make a crater on impact, but could really hurt if you got hit. Gravity makes the penny ACCELERATE toward the ground at around 10 m/s2. What is the penny’s VELOCITY after:– 1 second– 5 seconds– 15 seconds– 1 minute

For reference, a car traveling 60 mph travels about 27 m/s!

• A drag racer accelerates his vehicle quickly over a ¼ mile to beat his competitor. If the driver ACCELERATES at 20 mph/s, what is their speed after:–1 second–5 seconds–10 seconds

• If the drag racer from the previous problem is travelling at 200 mph at the end of the race, they need to brake quickly to stop. If the driver manages to stop in 20 seconds, what is his ACCELERATION? Be careful – acceleration includes both RATE and DIRECTION!