Instantaneous Velocity versus Average Velocity over a Short Time
After analyzing our data in Microsoft Excel, we have the (t,y) graph on the left side of the board. We would like to get the velocity at several places along this graph. Unfortunately, with a constantly changing slope, it isn't so easy. We'd have to draw a lot of tangent lines and that would be very difficult to do by hand. Calculus was invented to help us accomplish such things.
We do have one thing that we can do. We can take average slopes over very short time periods, like on the graph on the right. They would have equations like are listed at the right hand side of the board. This doesn't perfectly give the idea of the constantly changing slope of the left graph, but it gives an approximate idea. We are going to use Excel to accomplish this as well.
Instantaneous Velocity versus Average Velocity over a Short Time
After analyzing our data in Microsoft Excel, we have the (t,y) graph on the left side of the board. We would like to get the velocity at several places along this graph. Unfortunately, with a constantly changing slope, it isn't so easy. We'd have to draw a lot of tangent lines and that would be very difficult to do by hand. Calculus was invented to help us accomplish such things.
We do have one thing that we can do. We can take average slopes over very short time periods, like on the graph on the right. They would have equations like are listed at the right hand side of the board. This doesn't perfectly give the idea of the constantly changing slope of the left graph, but it gives an approximate idea. We are going to use Excel to accomplish this as well.