Linear Motion

Ch. 2.1-2.4

Neglecting Air Resistance• If Aristotle had neglected air resistance, things in

physics would be a lot different• Demo

– Paper --> crumpled paper– Paper vs crumpled paper side by side– Paper vs book (side by side, underneath, on top)

• Although air resistance and the shape of moving objects are important, we will ignore them for the time being and focus on the relationships between speed, velocity, and acceleration.

Jokes• Do you remember a joke better if you hear it or if you

hear it and then tell it?• A lot of checking with your neighbor.

Objectives

1. Explain the idea that motion is relative

2. Instantaneous vs. average speed

3. Velocity vs. speed

4. Define acceleration

Motion is relative

30 km/s relative to the sun 8 km/s relative to the earth

300 km/s relative to the ground

Relative: with respect to

For this class, when discussing speed, we mean speed relative to surface of the earth, or the ground.

What is Speed?• Speed is a measure of how fast something is moving

– Distance compared to time.

• Who’s been on a road trip?• Average Speed = distance/time

= change / = “per” km per hour• Stride across floor---1m/s

• Draw diagrams to help you with word problems• Road trip: traveled 200 miles in 4 hours. What’s the average

speed? Check with your neighbor before raising hand…• Avg. speed = 200 mi / 4 hr ---> 50 mph

• What do speedometers tell us?• Instantaneous speed:

– the speed at any one instant

• How is this different from average speed?• Instantaneous vs. Average Speed

More practice• Draw a diagram when figuring out the next couple of

problems, then do the math. Check with neighbor when finished.

1. The odometer on your car reads 50 miles at the beginning of a trip and 200 at the end. You drive for a total of 3 hours. What is your average speed? (draw a diagram to help you answer)

¯ 200 - 50 = 150 miles

¯ 150miles/3 hours = 50 mph

2. If an odometer reads 0 at the beginning of a trip, 35km a half an hour later, what is the average speed?

– 35km/0.5h = 70km/h

More Practice

1. If a cheetah can maintain a constant speed of 25m/s, it will cover 25 m every second. At this rate, how far will it travel in 10 seconds? 1 minute? (Draw it out!)

– Distance = velocity(time)– (25m/s) x (10s) = 250m– (25m/s) x (60s) = 1500m

• Review

Check Questions

• Q: If you ride a bike a distance of 5m in 1s, what is your speed?

• A: 5m/s

• Q: For 10m in 2s?

• A: 5m/s

• Q: For 100 m in 20s?

• A: 5m/s

Interesting tidbit . . .Downhill skiers attain speeds of 70-80 mph on winding

runs inclined at about 10-15°. A Speed of 70 mph

is102.7ft/s,which means a skier covers 10.3 ft in 0.1 s.

Even quicker are skiers who ski slopes inclined up to 50º at

speeds up to 139 mph or 204 ft/s. At this speed a skier

could cover the length of a football field in 1.5 s. This is

faster than a skydiver falls in spread eagle position!!.

Velocity• Velocity:

– Speed with direction

• If either speed or direction changes --> change in velocity

Velocity Checkpoint(draw a diagram to help and check w/

neighbor)• If an airplane travels 500 km due north in 1 hour,

what is its velocity?– 500 km north/ 1hr = 500 km/hr north

• If it travels 250 km due south in 1/2 hr, what’s its velocity?– 250 km south/0.5 hr = 500 km/hr south

• What about 125 km east in 1/4 hr?– 125 km east/0.25 = 500 km/hr east

• If a car travels at the SAME speed while driving in a circle, is it changing velocity?

Acceleration

• Acceleration• CHANGE in velocity/change in time• a = v/t

• “/” means divided by

Let’s refresh our memories. . .

• How do we determine average speed? Somebody write it on the board – Average Speed = distance/time

• What is velocity?– Speed with DIRECTION

• If the speedometer of a car reads a constant speed of 40 km/h, can you say that the car has a constant velocity? Why or why not?

More review (use white boards)• What is the average speed of a racehorse

that runs 210 meters in 7 seconds?– 210m / 7s = 30m/s

• It takes Mr. Ward 30 minutes to run from MC to Redwood HS. The distance is 7 kilometers. What is his average speed?– 7km / 0.5hr = 14 km/h

More review

• An automobile travels 400 km due south in 5 hours. What is its velocity?– 400km south / 5 hr = 80 km/hr SOUTH

• Do we remember what acceleration is?– Change in velocity divided by a change in time

Acceleration

• Suppose you are watching a race from the sidelines and the cars are in a straight away, all traveling at a constant 120 mph. You friend says, “Wow, look at the acceleration of those cars!” Is he/she correct in making this statement?

We can FEEL the acceleration

Causing Acceleration

• What are three things that we can do in a car to cause a change in acceleration?

1. Accelerator pedal2. Brakes3. Steering wheel

• If you round a corner in a car and keep your speed a constant 60 km/hr, are you accelerating? Check your neighbor.

Acceleration

NOT simply a change in speed!!!

Check Acceleration

• What is the acceleration of a car that goes from 0 to 100 km/h in 10 s?

• (100 km/h) / (10 s) = (10 km/h)/s– **Note that the unit for time enters twice. Why?

• once for the unit of speed and AGAIN for the interval time in which the speed is changing

• What is the acceleration of a dog that moves from 0 to 10 m/s in a time of 1 s?

• (10 m/s ) / (1 s) = (10 m/s)/s

Concept CheckDraw this out then check your neighbor

1. Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then from 45 to 50 km/h. What is it’s acceleration?

• Speed increases by 5 km/h during each 1-second interval. Therefore, acceleration is 5 km/h/s

– Or…. You could divide 15 km/h by 3 seconds….

Concept Check Draw this out then check your neighbor

1. In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h. At the same time, a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle?

• The car and truck both increase their speed by 15 km/h during the same time interval (5 s), so their acceleration is the same.

• Acceleration = speed/ time• (15 km/h) / (5 s) = 3 km/h/s

More Practice

• You are pedaling your bike at a constant speed of 15 km/hr. You decide to step it up a notch and increase your speed to 35 km/hr over 5 seconds. What is your rate of acceleration? (remember the units)• 35 km/hr - 15 km/hr = 20 km/hr• 20 km/hr divided by 5 seconds = 4 km/hr/s

Last one….• A cheetah is chasing a gazelle. The cheetah is running

at a constant speed of 60 km/hr, but can’t seem to catch the gazelle. Within 6 seconds the cheetah is running at the speed of 72 km/hr. What is the rate of acceleration? • 72 km/hr - 60 km/hr = 12 km/hr• 12 km/hr divided by 6 seconds = 2 km/hr/s

• How many seconds will it take the cheetah to go from 60 km/hr to 84 km/hr?• a = v/t• t (a) = v• t = v divided by acceleration• t = 24 km/hr divided by 2 km/hr/s• 12 seconds to go from 60 km/hr to 84 km/hr

Did we obtain our objectives?

1. Explain the idea that motion is relative

2. Instantaneous vs. average speed• What is the equation for avg. speed?

3. Velocity vs. speed

4. Define acceleration• What is the equation for acceleration?

Domino Prelab• Purpose: rewrite in own words from handout—

remember three parts• Hypothesis: What kind of spacing between

dominoes will allow for the maximum average speed? (small, medium or large)

• Materials: List from handout• Procedure: highlight in handout• Results:

– Copy “Data Table A” (only need room for 4 trials) from your handout into lab NB

– Copy “Fig A” from handout into lab NB (change x-axis to Average Spacing in cm)