Help! I've fallen and I can't get up!
To solve this problem, the big-picture approach is to integrate the acceleration equation to find the velocity equation and then integrate the velocity equation to find the position equation. Along the way, the "+c" also needs to be solved for every time that an indefinite integral is taken.
The problem tells us that the acceleration of gravity pulling the calculator down is -10 m/s^2, so the second derivative of position is -10. When we integrate this, we have a constant on the right side of the equation because of an indefinite integral, so we plug in the initial value of time and velocity and calculate that the value of c is 5.
Plugging in the value for c into the velocity equation, our velocity equation is now complete. But we still need to find the position equation, which is the integral of the velocity equation we just found. We integrate both sides of the velocity equation and we once again have a constant on the right side of the equation. Plugging in the initial values of time and height above the ground, we calculate that c is 1. Plugging this back into the position equation, our position equation is now complete.
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