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.
 
 

Any object on the surface of the Earth is under constant acceleration: Gravity! More about gravity in the next module...