Chapter Four: Motion

4.1 Position, Speed and Velocity

4.2 Graphs of Motion4.3 Acceleration

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.

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

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.

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.