Quiz Next Week Monday & Tuesday

The name of the COSMOS episode is the 3rd in the series “When Knowledge Conquered Fear”

https://www.youtube.com/watch?v=YHLV_Zyd64U

Study the notesLearn to solve for a

speed problems& Acceleration problems

See Word Document for possible questions on Quiz

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

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 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

4.2 Graphs of Motion Constant speed means the speed

stays the same. An object moving at a constant speed

always creates a position vs. time graph that is a straight line.

4.2 Slope The steepness of a line is

measured by finding its slope. The slope of a line is the ratio of the “rise” to the “run”.

4.3 AccelerationAcceleration is the rate at which your

speed (or velocity) changes.If your speed increases by 1 meter per second (m/s) for each second, then your acceleration is 1 m/s per second.

4.3 AccelerationAcceleration is easy to spot on a speed vs. time graph.Acceleration causes the line to slope up on a speed vs. time graph.

4.3 AccelerationIf the hill is steeper, the

acceleration is greater.

4.3 AccelerationThere is zero acceleration at constant speed

because the speed does not change.

4.3 AccelerationSpeed and acceleration

are not the same thing. You can be moving (non-

zero speed) and have no acceleration (think cruise control).

You can also be accelerating and not moving!

A falling object begins accelerating the instant it is released.

4.3 AccelerationAcceleration describes how quickly speed changes.

Acceleration is the change in speed divided by the change in time.

4.3 Speed and accelerationAn acceleration of

20 km/h/s means that the speed increases by 20 km/h each second.

The units for time in acceleration are often expressed as “seconds squared” and written as s2.

Can you convert this rate using conversion

factors?

Solving Problems

A sailboat moves at 1 m/s.

A strong wind increases its speed to 4 m/s in 3 s.

Calculate acceleration.

1. Looking for: …acceleration of sailboat

2. Given: …v1 = 1 m/s; v2 = 4 m/s; time = 3 s

3. Relationships: a = v2 – v1/t

4. Solution: a = (4 m/s – 1 m/s)/ 3 s

= 1 m/s2

Solving Problems

4.3 Acceleration on motion graphsThe word “acceleration” is used

for any change in speed, up or down.

Acceleration can be positive or negative.