Calculus Extension of Angry Bird Lab (2/2)
The derivative can be scary at first. I wanted to take it in 3 different ways: Graphically, with the numbers we got from the (t,y) equation in the Angry Bird lab, and symbolically.
If you understand the three graphs here, you understand that the velocity graph is a plot of the slope of the position graph at each time. In the lab, you took the slope by actually doing the slope formula between data points.
The derivative lets us do this not by getting the slope between data points, but transforming the entire function. In a Calculus class you'll learn to do this by implementing the rule in purple at the bottom center of the board.
Please go through the center and right hand columns and see if you can follow them. With practice, you'll be great at taking derivatives. The key thing now is that you know why we do it. The slope at every point on a (t,y) graph is the velocity. The slope at every point on a (t,v) graph is acceleration.
Note that my acceleration is somewhat less than the predicted -9.8 m/s². This is because of experimental error.
The trick of writing the equation with t^1 and t^0 was suggested by a 6th Period Student at Manchester HS in the 2018-19 school year
Calculus Extension of Angry Bird Lab (2/2)
The derivative can be scary at first. I wanted to take it in 3 different ways: Graphically, with the numbers we got from the (t,y) equation in the Angry Bird lab, and symbolically.
If you understand the three graphs here, you understand that the velocity graph is a plot of the slope of the position graph at each time. In the lab, you took the slope by actually doing the slope formula between data points.
The derivative lets us do this not by getting the slope between data points, but transforming the entire function. In a Calculus class you'll learn to do this by implementing the rule in purple at the bottom center of the board.
Please go through the center and right hand columns and see if you can follow them. With practice, you'll be great at taking derivatives. The key thing now is that you know why we do it. The slope at every point on a (t,y) graph is the velocity. The slope at every point on a (t,v) graph is acceleration.
Note that my acceleration is somewhat less than the predicted -9.8 m/s². This is because of experimental error.
The trick of writing the equation with t^1 and t^0 was suggested by a 6th Period Student at Manchester HS in the 2018-19 school year