Motion

Chapter 11

What is motion?

It’s an object that has a direction

It also tells how fast the object is going

It also tells a location at a given time.

Puttin’ a frame on it

To describe motion accurately, a frame of reference is needed.

A frame of reference is a system of objects that are not moving with respect to one another.

So who is really moving? All depends on your frame of reference.

How fast you moving?

How fast are the passengers of the train moving?

There are actually many correct answers because movement is relative.

Relative motion: Movement in relation to a frame of reference.

So what frame do I go with?

Once again, it all depends on what you want to know.

What would you choose if you are sitting in a bus and want to know how fast you are going relative to the ground?

What about if you walk to the back of the bus?

Know what your looking for and find a reference.

We’re going the distance

Distance: Length between two points.

Always good to express distances in units that are best suited to what you want to know.

SI unit for distance is meters Long distances are measured in Kilometers (1000 m) Medium distances are Meters Short distances are Centimeters (100 cm in a m)

Displacements

Displacement: Direction from the starting point and the length of a straight line from the starting point to the ending point.

Typically used when giving directions.

Why?

What’s your Vector, Victor?

Displacement is a vector

Vector: a quantity that has magnitude and direction. Magnitude: can be size, length, or amount.

Arrows on a graph/map are used to represent vectors The length of the arrow shows the magnitude

Displacement in a line

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

Example

What if it isn’t a straight line?

When two (+) displacement vectors have different directions, they may be combined by graphing.

Example

The vector I drew in red is the RESULTANT VECTOR: The sum of two or more vectors.

Speed

Speed: Ratio of the distance an object moves to the amount of time the object moves.

SI Unit: Meters per second (m/s)

Just like before, need to use logical units.

1st Type of Speed

Average Speed: How fast something moves for the duration of a trip.

There is a formula to help figure this out: v= d/t v= average speed d= total distance t= total time

Problem 1

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

1. What do you have?2. What are you answering?

Problem 2: Manipulate the formula

How far does a jogger run in 2 hours (7200 seconds) if his average speed is 6 m/s?

1. What do you have?

2. What are you answering?

Problem 3: Manipulate for distance

How long does it take a swimmer to complete a 100 meter swim if his average speed is 10 m/s?

1. What do you have?

2. What are you answering?

2nd type of speed

Instantaneous speed: Tells you how fast you are going at a particular moment

Speedometer can measure this

Graphing Speed

Also called a distance-time graph

The slope of the line is the speed Remember Slope is figured by Rise/Run

Distance is on Y-axis Time is on X-axis

Velocity

Velocity: The speed and direction in which an object is moving

Velocity describes both speed and direction, thus making it a vector

Just like with our displacement vectors, velocity vectors uses arrows of different lengths. Longer= Faster velocity Shorter= Slower Velocity

Combining Velocities

Two or more velocities add by vector addition

Example 1: Same Direction Velocities

Example 2: Different Direction Velocities In order to get the angle we need to use the

Pythagorean theorem: a2 + b2 = c2

C is the hypotenuse, this is the part we want to find

Acceleration

Acceleration: The rate at which velocity changes

Acceleration can be a change in speed, direction, or both.

It’s a vector

Changes in Speed

Typically we think of acceleration as an increase in speed.

It can also be a decrease in speed or deceleration

Can be caused by positive (increase) change or a negative (decrease) change in speed

Example: A car

I’m freefallin’

Free fall: the movement of an object toward Earth solely because of gravity

Remember: Velocity is m/s The units for acceleration is m/s/s or m/s2

Gravity is 9.8 m/s2

This means that each second an object is in free fall, its velocity increases by 9.8 m/s2.

Changes in Direction

You can accelerate without changing speed

Going around a curve in a car/bike or riding a carousel are both accelerating with a constant speed.

Changes in Both

Example: Roller coaster

Example: Winding Road

Constant Acceleration

Constant Acceleration: a steady change in velocity

Which means, the change of velocity is the same each second

Calculating Acceleration

You can calculate acceleration by dividing the change in velocity by the total time

a= (vf-vi)/t a= acceleration vf= Final velocity vi= initial (starting) velocity t= time

Problem

A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball?

What do we know? What are we solving?

Acceleration Graphs

Also called velocity-time graphs

Y-axis is speed X- axis is time

Slope is acceleration

Constant acceleration on Graph

Constant acceleration is represented by a straight line called a linear graph.

Positive acceleration goes upwards

Negative acceleration goes downwards

A straight line on an acceleration graph represents a constant velocity

Distance-Time Graphs

Accelerated motion is represented by a curved line on a distance-time graph

This is also called a non-linear graph

You can check this by calculating the slope between two points.

Instantaneous Acceleration

Instantaneous acceleration is how fast a velocity is changing at a specific instant.