Chapter 4 MOTION

Chapter Four: Motion

4.1 Position, Speed and Velocity

4.2 Graphs of Motion4.3 Acceleration

Who Wins?????Racer with the fastest speed?Racer with the shortest elapsed time?

What is motion?What is speed?How is speed different from velocity?

Battery BuggyAfter watching the buggy, how is it’s motion different/similar to a 100 meter sprinter? What if the batteries were close to dead?

Motion is RelativePerception of motion by humans is always related to nearby objects, a reference point

Even if there is motion, but no nearby reference, motion is not perceived by humans.

Unit

Motionis defined as the

change in position of an object over time when compared to a reference point.

Moving?

At rest? Object does not change position relative to reference point.

Speeding Up? Object travels greater distance in later time periods.

Slowing Down? Object travels less distance in later time periods.

Constant Speed? Object travels same distance in later time periods.

4.1 Position, Speed and VelocityPosition is a variable given relative to

an origin.The origin is the place where position equals 0.

The position of this car at 50 cm describes where the car is relative to the track.

4.1 Position, Speed and VelocityPosition and distance are similar but

not the same.If the car moves a distance of 20 cm to

the right, its new position will be 70 cm from its origin.

Distance = 20 cm

New position

4.1 Position, Speed and VelocityThe variable speed describes how

quickly something moves. To calculate the speed of a moving

object divide the distance it moves by the time it takes to move.

Triangle Trick:

4.1 Position, Speed and VelocityThe units for speed are distance units

over time units.This table shows different units

commonly used for speed.

4.1 Average speed

When you divide the total distance of a trip by the time taken you get the average speed.

On this driving trip around Chicago, the car traveled and average of 100 km/h.

4.1 Instantaneous speed

A speedometer shows a car’s instantaneous speed.

The instantaneous speed is the actual speed an object has at any moment.

How far do you go if you drive for two hours at a speed of 100 km/h?

1. Looking for: …distance

2. Given: …speed = 100 km/h time = 2 h

3. Relationships: d = vt

4. Solution: d = 100 km/h x 2 h = 200 km

= 200 km

Solving Problems

Example: If it took you two hours to travel from mile marker 187 to mile marker 87 on I-44 (Rolla to Springfield) your average speed would be….

Speed = distance traveledtime

Speed = 100 miles 2 hours

Speed = 50 miles hour

Speed = 50 miles/hr or MPH

Example Question1. What is the average speed of a cheetah that sprints 100 meters in 4 seconds?

2. How about if it sprints 50 m in

2 seconds?

Example QuestionIf a car moves with an average speed of 60km/h for an hour, it will travel a distance of 60 km. (a) How far would if travel if it moved at this

rate for 3 hours? (b) How far would it travel if it moved at this

rate for 4 hours and 20 minutes?Use the “Triangle” trick to write equation for

distance

Example QuestionIf a car moves with an average speed of 60km/h … What time would it take for the car to

travel 300 km? What time would it take for the car to

travel 400 km?

Use the “Triangle” trick to write equation for time

4.1 Vectors and velocity Position uses positive and negative

numbers. Positive numbers are for positions to

the right of the origin and negative numbers are for positions to the left the origin.

4.1 Vectors and velocity

Distance is either zero or a positive value.

4.1 Vectors and velocity We use the term velocity to

mean speed with direction.

interval timentdisplaceme Velocity

Displacement is a change in positionWhat is the distance traveled? What is the displacement?

Can you calculate the average speed of the skier at D?Can you calculate the average velocity of the skier at D?

Java

0 10 20 30 40 50-10-20-30-40-50 0 10 20 30 40 50-10-20-30-40-50

0 10 20 30 40 50-10-20-30-40-50 0 10 20 30 40 50-10-20-30-40-50

4.1 Keeping track of where you are Pathfinder is a small robot sent

to explore Mars.

It landed on Mars in 1997.

Where is Pathfinder now?

4.1 Keeping track of where you are Pathfinder keeps track of its

velocity vector and uses a clock. Suppose Pathfinder moves

forward at 0.2 m/s for 10 seconds.

What is Pathfinder’s velocity?

4.1 Keeping track of where you are Suppose Pathfinder goes

backward at 0.2 m/s for 4 seconds.

What is Pathfinder’s change in position?

4.1 Keeping track of where you areThe change in position is the

velocity multiplied by the time.

4.1 Keeping track of where you areEach change in position is added up

using positive and negative numbers.Pathfinder has a computer to do this.

4.1 Maps and coordinates If Pathfinder was crawling on a straight

board, it would have only two choices for direction.

Out on the surface of Mars, Pathfinder has more choices.

The possible directions include north, east, south, and west, and anything in between.

4.1 Maps and coordinates A graph using north−south and

east−west axes can accurately show where Pathfinder is.

This kind of graph is called a map.

Street maps often use letters and numbers for coordinates.

4.1 Vectors on a map Suppose you run east for 10

seconds at a speed of 2 m/s. Then you turn and run south at the

same speed for 10 more seconds.

Where are you compared to where you started?

4.1 Vectors on a mapTo get the answer, you figure out your east−west changes and your north−south changes separately.

origin = (0 , 0)

4.1 Vectors on a mapYour first

movement has a velocity vector of +2 m/s, west-east (x-axis).

After 10 seconds your change in position is +20 meters (east on x-axis).

d = v x t d = 2 m/s x 10 s = +20 m

4.1 Vectors on a mapYour second

movement has a velocity vector of −2 m/s north−south (y-axis)

In 10 seconds you move −20 meters (south is negative on y-axis)

d = 2 m/s x 10 s = -20 m New position = (+20 , -20)

A train travels at 100 km/h heading east to reach a town in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now?

1. Looking for: …train’s new position

2. Given: …velocity = +100 km/h, east ; time = 4 h …velocity = -50 km/h, west ; time = 4 h

3. Relationships: change in position = velocity × time

Solving Problems

4. Solution: 1st change in position:

(+100 km/h) × (4 h) = +400 km

2nd change in position: (−50 km/h) × (4 h) = −200 km

Final position: (+400 km) + (−200 km) = +200 km The train is 200 km east of where it started.

Solving Problems

4.3 Curved motion

Circular motion is another type of curved motion.

An object in circular motion has a velocity vector that constantly changes direction.