When moving in a car at the speed of 50 miles/hour, you understand that the car will go a distance of 50 miles in one hour, if it maintains a constant speed. In the same way, if you are at 50 miles/hour and travel 0.5 hours, you will have traveled 25 miles (provided the speed is the same all the time!)

In general then:

Normally we use speed and velocity interchangeably in our day-to-day conversations. In reality these two things have different meanings. We always associate a direction to velocity, while speed is just a number. But how do we understand a quantity which has direction? For that, we first need to have a good idea of displacement and path!
 
 

You walk north to your school which is three miles from your house. Then you turn around and walk south two miles back to your starting point (home). How far have you moved? How long have you walked?

There are two ways of looking at this: One is by adding the two changes in position as scalar quantities and the other is by adding them as vector quantities. Scalar quantities are measurements that only include how big they are. They don't take into account direction. A physics book will tell you that they are measurements of magnitude. Vector quantities are measurements that include both magnitude and direction. So how do you describe your motion? The distance (a scalar) that you walked to school and straight back was 6 miles. You just add the magnitudes of the two motions. Your displacement, a vector, has to be added up a little differently because you have to account for the direction. Displacement is your position compared to a reference point. One way of finding your displacement is by using arrows. Your displacement in your trip to school and back home was ZERO!
 

Use the grid below to follow your trip from home (yellow circle) to school (red circle), and to a friend's house (blue circle) and stopping at the market (green circle) on the way back home to pick up eggs for your mom. What is your displacement?  What was the distance traveled? (Each little square is a mile.)

Suppose you went for a walk and the green arrows represent your path, or the distance traveled, and the red arrow represents your displacement. The displacement between any two points is a "vector" directed from one point to the other (start to finish). The magnitude of this vector is its length. What is the magnitude of your diplacement in this trip?
 
 

What have we been doing all this time, going from home, to school, and going around? We have been in motion. When we start to think about where we are at different times, we have MOTION. There are different kinds of motion depending on how your position changes with time. For example, when we are not going anywhere during some time, we are at rest. Rest is also a kind of motion, according to our definition.

Now it would be a good time to complete worksheet1.
 

Motion along one direction: Most of the time we will be thinking about motion in one direction only, like cars on a freeway, where there are only two lanes and you can only go north or south. In the case of the two cars below both are going on the same direction, but with different velocities. The numbers below are the number of meters since we started measuring their movement.
 
 

Classroom activity: Use 1 hotwheel or toy car for this experiment. With a measuring tape and a stopwatch, record the position and the elapsed time of the little car when:

•  it is at rest - not going anywhere
•  it is moving at constant velocity  - moving at constant speed without changing the direction
•  it is in uniformly accelerated motion - constantly accelerating!

http://www.glenbrook.k12.il.us/gbssci/insti/lesson1.html

What is acceleration? Acceleration is the name given to the variation in the rate of change of the velocity. Take a look at this web page http://www.glenbrook.k12.il.us/gbssci/insti/lesson2.html to see how we can distinguish between accelerated and "non-accelerated" motion.

After reading and understanding this web page and the problems of Ms. Oyle, let's make some graphs based on what we have learned. This is worksheet 3.
 
 

Acceleration is a vector quantity, (i.e., it has a direction and magnitude!) that measures any change in velocity. That means speeding up, slowing down, and turning. Most people use the term only to mean speeding up, but when slowing down, we are applying negative acceleration to the movement. This is a very key concept for everything else we will learn, so keep in mind that: Acceleration is any change in velocity and that includes speeding up, slowing down, and turning.

A good short definition for acceleration is the rate of change in velocity. Suppose that at a certain instant a car has velocity (don't forget that velocity has direction!) v_i, and that at a later time t, its velocity is v_f, in this context the average acceleration of the car is a = (v_f-v_i)/t

Note: people normally use bold font to note vectors. Also we call v_i initial velocity and v_f final velocity.

You probably have an intuitive understanding of acceleration. You can feel changes in speed and direction. That's why fast cars and roller coasters are so much fun. Speeding around those tight turns and curves, or accelerating from 0 to 60 miles per hour in a few seconds causes your body to be pushed and pulled as the vehicle changes velocity and your body is forced to catch up.

So if you are stopped at a red traffic light, with v_i=0, and after 60 seconds you are at 12m/s then your average acceleration in this period was 12 m/s².

The bottom line here is that all falling objects are subjected to the same acceleration pulling them towards the Earth: gravity. In the same way an engine accelerates a car, gravity accelerates objects when they fall. The magnitude of the velocity of a falling body is shown in the graph below. If you calculate the "rate of change" of the velocity in any time interval in this plot you will see that the rate of change is g=9.8 m/s², the acceleration due to gravity.

 

Observe that the velocity-time data above reveal that the object's velocity is changing by 10 m/s each consecutive second. That is, the free-falling object has an acceleration of 10 m/s/s.

Assuming that the position of the free-falling ball dropped from a position of rest is shown every 1 second, then the velocity of the ball can be shown to increase as depicted in the diagram at the right.

(NOTE: The diagram is not drawn to scale - it would not take more than two seconds for a ball to drop from shoulder height to toe height.)

Now it may be a good time to check out other pages. Let's go see what happens when elephants and feathers fall on: http://www.geocities.com/Athens/Academy/9208/efff.html

After this trip, there is a worksheet to fill about free fall: Worksheet4

I guess now we all understand what is going on whe things fall in ONE direction. What about baseballs and cannon balls???? These things undergo what we call projectile motion.