MotionThe physics of movement

Kinematics

Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations.

In this lesson, we will investigate the words used to describe the motion of objects. That is, we will focus on the language of kinematics.

What words do you use to describe motion?

Scientific words we will use in this unit

We will study such terms as: Scalars Vectors Distance Displacement Speed Velocity Acceleration.

Describe the following:

Image 1

Image 2

Image 3

Image 4

Image 5

Image 6

Image 7

Image 8

The terms used to describe motion can be broken down into two categories:

Scalar are quantities that are fully described by a numerical value alone.

Vector are quantities that are fully described by both a numerical value and a direction.

Scalar or Vector ?

A. 5 m ScalarB. 30 m/sec East VectorC. 5 mi., North Vector D. 20 degrees Celsius ScalarE. 256 megabytes ScalarF. 4000 Calories Scalar

To test your understanding of this distinction, consider the following quantities listed below. Categorize each quantity as being either a vector or a scalar.

Distance and Displacement

your home

your school

A displacement has

Size = length of this arrow

displacement from home to school

displacement from home to school

Displacement and distanceTo go to school from home...

size & direction.

Distance = length of path you travelled

( size of displacement)

l1l2l3

Displacement and distanceTo go to school from home... your

home

your school = l1 + l2 + l3

Displacement

There is a distinction between distance and displacement.

Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.

Distance traveled (dashed line) is measured along the actual path.

Displacement

©2008 by W.H. Freeman and Company

Left:

Displacement is positive.

Right:

Displacement is negative.

The displacement is written:

SpeedHow fast is it really going?

Definition of Speed

Speed is generally used to describe how fast something happens, but it is defined as ‘the rate at which an object moves over distance, over a variable amount of time’.

Speed has a variety of units depending on the units used for distance and time.

Speed Formulas

average speed = distance time

distance = average speed x time  time = distance average speed Note: 1 kilometre (km) = 1000

metres

An easy way to remember the formulas

Distance

Time Speed

Example: If you are working out distance you cover the word distance and you know the equation is:

average speed x time

Example: questions 1 to 4

1. Speed = a. Distance (9000 m) ÷ Time (12.12 seconds) = 742.57 m/s

2. Speed=a. Distance (528 m) ÷ Time (4 seconds) = 132 m/s

3. Distance = a. Average Speed (96 m/s) × Time (17 seconds) = 1632

m

4. Time = a. Distance (500, 000m) ÷ Average Speed (700 m/s) = 714.28

s

Speed

Distance

Time

Example: questions 5 to 8

5. Time = a. Distance (350 km) ÷ Speed (80km/hr) = 4.375 hrs

6. Time =b. Distance (450 km or 450,000m) ÷ Speed (120 m/s) = 3750 s

7. Speed = a. Distance (1km or 1000m) ÷ Time (20 minutes or 1200 s) = 0.83 m/s

8. Distance = b. Average Speed (6 m/s) × Time (3 minutes or 180 s) = 1080 m

9. Distance = a. Average Speed (100 km/hr or 27.7m/s*) × Time (10

minutes or 600 s) =

10. Time = b. Distance (20 km or 20,000m) ÷ Average Speed (40 m/s) = 500 s

Example: questions 9 to 10

100 km/hr

100,000 m/hr

1666 m/min

27.7 m/s

*Conversion

Covert to meters

Covert to meters per

minute

100km x 1000

100,000 ÷60

Covert to meters per

second

1666 ÷60

Conversion complete

Graphing speed Distance vs. Time Graphs

Remember

average speed = distance time

distance = average speed x time 

time = distance average speed

Remember calculations involving speed involve:

Distance Time

Remember the story The Three Little Pigs?

•The wolf started from his house.• Travelled to the straw house.• Stayed to blow it down and eat dinner.• Travelled to the stick home.• Again, stayed to blow it down and eat dinner.• Travelled to the brick house.• Dies in the stew pot at the brick house.

a) How many stops does the boat make?

b) What is the boat’s average speed for the whole trip?

c) What is the highest speed the boat reaches?

Activity: Tell Me A Story

Reading motion graphs

Distance vs. Time

Velocity (speed) vs. Time

Acceleration vs. Time

ConstantAccelerating at 1m/s/s

No Acceleration

Increasing Acceleration

Deceleration

Acceleration

Acceleration

Acceleration refers to the speeding up or slowing down.

Deceleration (retardation) refers to a negative acceleration.

Technically, acceleration is change of velocity with respect to time.

Acceleration = change in speed time

Calculating Acceleration

A motorist gets in her car & accelerates up to 60km/h in 5s. What is her average acceleration?

Note: generally the SI unit for acceleration is m/s/s.

Activity: Acceleration Calculations

Acceleration = change in speedtime

= final speed – initial speed time

= (60 – 0)km/h 5 s= 12km/h/s or 12km/h s-1

If answer was negative, then this would be deceleration.

1. A car changes its velocity by 30 m/s in 5 seconds, what is the acceleration of the car?

2. A bike starts from rest and accelerates to 20 m/s over a period of 6 seconds. What is the acceleration of the car?

3. A man moving at 2 m/s accelerates at a rate of 3 m/s2 for 2.5 seconds. What is the new velocity of the man?

4. A car decelerates from 60 m/s to 20 m/s at a rate of -5 m/s2. How long does this deceleration take the car?

6 m/s2

3.33 m/s2

9.5 m/s

8 seconds

Practice Questions

Centripetal Acceleration

Acceleration directed toward the center of circular path

Newtons laws of Motion

Newtons Third Law

To every action there is always an equal and opposite reaction

Problem

What would happen if you tried to push a desk while on a skateboard?

Newton’s Third Law

For every action there is an equal and opposite re-action.

What Does this mean? For every force there is a reaction force that is equal in

size, but opposite in direction. That is to say that whenever an object pushes another object it gets

pushed back in the opposite direction equally hard.

Can you explain how action-reaction forces are involved in the following pictures?

The rocket flying up through the air

As the rocket flies up through space, exhaust exits from the back of the rocket. The exhaust acts on the rocket pushing it upwards. The rocket has an equal and opposite action on the

exhaust, expelling it downwards.

Pushing the shopping cart The man acts on the shopping

cart, propelling it forward. The shopping cart acts on the man’s hands, pushing back on his hands with a reaction that he can feel. However, while he feels a force pushing him backwards the man does not actually move backwards, since he can overcome that force with his feet and legs.

The dolphins swimming in the water

As the dolphins swim through the water, they act on the water, pushing it aside and backwards. The water exerts an

equal and opposite reaction on the dolphins, propelling them forward.

Action

Reaction

The hammer hitting the nail

The hammer acts on the nail, driving it into the

wood. The nail acts on the hammer, pushing back on the head of the hammer with a reaction that can

be felt by the hand holding the hammer.

As the nail is driven into the wood, the nail acts on the wood, but the reaction force of the wood on the nail is unbalanced,

allowing the nail to accelerate into the wood.

Revision for Test

You need to be able to:

Interpret the following types of graphs: ▪ Displacement vs. Time ▪ Speed (velocity) vs. Time ▪ Acceleration vs. Time

Be able to use the following ▪ average speed = distance time▪ distance = average speed x time▪ time = distance average speed

Calculate Acceleration:

Remember to use the triangle

Acceleration = change in speedtime

= final speed – initial speed time