Now its time to take a little more formal look at what we have been doing experimentally.

The part of physics that deals with the position and velocities of moving objects is called kinematics .

Our measurements of the positions of objects in free fall as a function of time is a way to experimentally define kinematics and from our experimental data the equations of kinematics can be recovered.

We have also been dealing with the concept of force although this has been an implicit part of our activities to date. For instance,

• We dropped balls from different heights and determined that some heights produced insufficient "force" to break our foil seal on the beakers. This implies that force combined with height above the earth's surface is an important quantity. So force x distance must be some relevant quantity. In fact, you should think about what you had to do when you went up the flights of stairs to get to this class. What were you working against?

• We also observed that when we used small steel balls, the foil seal broke much more easily from a lower height than when we used tennis balls. This implies that a "force" which is distributed over a certain area is also some relevant physical quantity.

Today we will see how force convolved with time produces different behavior. This is known as impulse

One way to describe kinematics is in a position vs time graph (the kind you are supposed to be making for the first homework assignment). An example is shown below

We can define the average velocity as the change in position divided by the change in time or:

Dp / Dt

which is the slope of the line in the position vs time graph. By graphical means we then determine the velocity at any time by determining the slope on the graph at that time. This is what calculus is about but we aren't doing that here.

Consider now the behavior of a fan cart, such as the one we are using in lecture today:

If we plot the velocity versus time of this cart we might get some data which looked like this:

Where we see that there are obvious changes in the velocity at various times. We are interested in understand what causes these changes in velocity.

The fan attachment exerts an almost constant force on the cart. What is the relationship between that strength of that force and the cart's acceleration?

Possible hypothesis

• Acceleration depends on the total force. More force, more acceleration?
• Acceleration only depends on the initial force (the impulse) and not on a continuous force. Initial acceleration to constant velocity or constant acceleration?
• Acceleration depends on mass. More mass, more acceleration?
• Acceleration is inversely proportional to the mass. More mass, less acceleration?