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course Phy 231
9/3 12You are asked to work out and explain, as homework, how the calculus-based formulation of uniform acceleration yields the same result.
Acceleration, in calculus terms, is the derivative of the velocity function (which, in itself, is a derivative of the position function). Smaller and smaller increments of the slope of the velocity graph are taken until the increments approach 0. The limit approached by that calculus process yields the instantaneous acceleration.
As a shortcut, the acceleration can be found by multiplying the velocity function expression by the power of the variable's exponent, then reducing that exponent by a magnitude of 1. Therefore, whenever the velocity function has a variable to the power of 1, the acceleration function will be a constant (which represents uniform acceleration).
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&#This looks very good. Let me know if you have any questions. &#