Chapter 11Motion

11.1 Distance & Dispalcement

Motion

Two parts of describing motion◦ 1. Speed◦ 2. Direction

Describing Motion

Definition - A system of objects that are not moving with respect to one another

Frame of Reference

Relative Motion• Definition – Movement in relation to a

frame of reference– For example, does a person sitting on a

moving train have motion? It all depends on the frame of reference

Tennis Ball Movement & Frame of Reference

Demonstration

The length of a path between two points

In other words, distance is the length of a path connecting an objects starting point and its ending point

SI unit for distance is the meter

Distance

Definition – The direction from the starting point and the length of a straight line from the starting point to the ending point

Example – What would your displacement be if you rode a rollercoaster?

Displacement

If you hit a home run in baseball, you would run from home plate, to each of the bases (1 through 3) and then back to home plate. If there is a distance of 30 meters between each of the bases, what is the total distance you run? What is your displacement?

Baseball Example

Definition – A quantity that has both magnitude (size, length or amount) and direction

Represented using arrows

Displacement is an example of a vector

Vector

When two displacements have the same direction, you can add their magnitudes

4 km E + 2 km E = 6 km E

Displacement along a straight line

0 1 2 3 4 5 6

4 km2 km

When two displacements have opposite directions, you can subtract their magnitudes

4 km E + 2 km W = 2 km E

Displacement along a straight line

0 1 2 3 4 5 6

4 km

2 km

When two or more vectors have different directions, they may be combined using graphing.

Displacement that is not along a straight line

How can we find the resultant vector?

The vector sum of two or more vectors

Can be used to show total displacement

Points directly from starting point to ending point

Resultant Vector

Distance v. Time Graph

11.2 Speed & VelocityMotion

How do we typically measure the speed of a

car?

The ratio of the distance an object moves to the amount of time the object moves.

SI UNIT◦ Meters per second, or m/s

Speed

Two types of speed

Average Speed Instantaneous Speed

Computed for the entire duration of the trip

Speed may change from moment to moment, but this tells you the average speed over an entire trip

Measured at a particular moment in time

Example: The speedometer in a car provides instantaneous speed

Average speed =

Or

◦ v = average speed◦ d = total distance traveled ◦ t = total time

v=

Average SpeedTotal Distance

Total Time

dt

While traveling on vacation, you measure the times and distances you travel. You travel 35 kilometers in 0.4 hours, followed by 53 kilometers in 0.6 hours. What is your average speed?

d = 35 km + 53 km = 88 kmt = 0.4 h + 0.6 h = 1.0 h

Average Speed Example 1

A person jogs 4.0 km in 32 minutes, then 2.0 km in 22 minutes, and finally, 1.0 km in 16 minutes. What is the jogger’s average speed in kilometers per minute? In km/ hour?

Average Speed Example 2

Use can use a distance-time graph to describe motion

Reminder – SLOPE◦ the change in the vertical axis value divided by

the change in the horizontal axis value

On a distance-time graph, slope is the change in the distance divided by the change in time (or speed)

Graphing Motion

A description of both speed and direction of motion

Velocity, like displacement, is a vector because it has both magnitude and direction

Velocity

Two or more velocities add by vector addition

When two velocities have the same direction, you can add their magnitudes

Combining Velocities

A man on the ground observes a train passing by. Through the train windows he sees a man running in the same direction as the train is moving. What is the apparent velocity of the man running on the train if the train is moving at 30 km/h and the man is running at 5 km/h?

Train Example

5 km/h

35 km/h

A plane is moving south at 100 km/hour. Wind is blowing from the east at 25 km/ hour. What is the resultant velocity of the plane? (HINT – draw a picture to help visualize the problem)

Plane Example

Warm-up Activity (Vector Addition)

11.3 AccelerationMotion

The rate at which velocity changes

Changes in:◦ Speed◦ Direction◦ Or both speed & direction

Acceleration is a vector (it has both magnitude and direction)\

SI Unit – meters per second per second (m/s2)

What is acceleration?

An acceleration that slows an objects speed

Negative acceleration

Example◦ As your car approaches a red light you step on

the break pedal to slow the car down. This causes the velocity of the car to change (it decreases) and thus the car decelerates.

Deceleration

The movement of an object toward Earth solely because of gravity

Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s2

Free Fall

Each second an object is in free fall, its velocity increases downward by 9.8 m/s

Free Fall (Continued)t = 0sv = 0 m/s

t = 1sv = 9.8 m/s

t = 2sv = 19.6 m/s

t = 3sv = 29.4 m/s

You can accelerate even if your speed is constant because acceleration also includes changes in direction

Example◦ If you ride a bike around a curve and maintain the

same speed, acceleration changes because your direction changes

Changes in Direction

Green Lantern Front Seat (Six Flags)

Describe the acceleration of the roller coaster as it reaches and just overcomes the first hill.

Roller Coasters…

A steady change in velocity

The velocity of an object moving in a straight line changes at a constant rate

Constant Acceleration

For straight-line motion:

Calculating Acceleration

Acceleration = Change in Velocity

Total Time

A = tvf - vi

vf = Final Velocityvi = Initial Velocity

What is the magnitude of the skydiver’s acceleration after 1 second? Between 2 and 3 seconds?

Acceleration Example #1t = 0sv = 0 m/s

t = 1sv = 9.8 m/s

t = 2sv = 19.6 m/s

t = 3sv = 29.4 m/s

A ball rolls down a ramp, starting from rest. After two seconds, its velocity is 6 m/s. What is the acceleration of the ball?

Acceleration Example #2

A = tvf - vi

vf = ? vi = ? t = ?

A = tvf - vi

Group Practice Activity

Complete the problem assigned to your group. You will be presenting your answer to the class.

A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration?

An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s2. What is its change in velocity during this time.

A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water? (Hint: Think “FREE FALL”)

A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boy’s hand? (Hint: Think “FREE FALL”)

The slope of a speed-time graph is acceleration

What is the formula for slope of a line?

Speed-Time Graphs

Time TimeTime

Sp

eed

Sp

eed

Sp

eed

Increasing Acceleration

Constant Acceleration

Decreasing Acceleration

How fast a velocity is changing at a specific instant

Instantaneous Acceleration

11.3 Warm-upSpeed-time graph

In the warm-up/ journal section of your binder sketch a speed-time graph of a car starting from rest, accelerating up to a speed limit of 35 mph, maintaining that speed for 10 seconds, then slowing again to a stop at a red light.