Calculus Extension of Angry Bird Lab (2/2) old
At the top left, I've written the equation that Google Sheets gave me for the Angry Bird's motion. This is a best fit parabola that takes into account the errors in all data points, so it's the best description of what the bird was doing.
We took the derivative to get a velocity function. Note that this came out linear
We took the derivative again to get an acceleration function. Note that this came out constant, with the value -9.074. In other words, the bird had a constant acceleration of -9.074.
Tracking back, we see that -9.074 in the velocity equation. So that term must be acceleration. Since the constant term in this equation must be a velocity, it's the original velocity. So apparently the equation for velocity at any time is v=v0+at.
Tracking back further, we see that the -9.074 isn't in the position equation, but half of it is. Also, the original velocity is there too. This gives us the position equation y=(1/2)at^2 + v0t + y0.
These two equations can be used to describe the velocity and position not just of this bird, but of ANY objects with constant acceleration like that which gravity gives.
For the record, the accepted value of the acceleration of gravity is -9.8 m/s/s. There was some experimental error in my measurement.
Calculus Extension of Angry Bird Lab (2/2) old
At the top left, I've written the equation that Google Sheets gave me for the Angry Bird's motion. This is a best fit parabola that takes into account the errors in all data points, so it's the best description of what the bird was doing.
We took the derivative to get a velocity function. Note that this came out linear
We took the derivative again to get an acceleration function. Note that this came out constant, with the value -9.074. In other words, the bird had a constant acceleration of -9.074.
Tracking back, we see that -9.074 in the velocity equation. So that term must be acceleration. Since the constant term in this equation must be a velocity, it's the original velocity. So apparently the equation for velocity at any time is v=v0+at.
Tracking back further, we see that the -9.074 isn't in the position equation, but half of it is. Also, the original velocity is there too. This gives us the position equation y=(1/2)at^2 + v0t + y0.
These two equations can be used to describe the velocity and position not just of this bird, but of ANY objects with constant acceleration like that which gravity gives.
For the record, the accepted value of the acceleration of gravity is -9.8 m/s/s. There was some experimental error in my measurement.