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Problem 50 Medium Difficulty

The equation of motion of a particle is, $ s = 2t^4 - 2t^3 + t^2 - t $ , where is in meters and is in
seconds.
(a) Find the velocity and acceleration as functions of .
(b) Find the acceleration after 1 s.
(c) Graph the position, velocity, and acceleration functions on the same screen.

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Video Transcript

he It's clear. So a new breed here. So we're gonna find the velocity and acceleration. So we have V A. T is equal to Ford t cubed minus 60 square plus two t plus one. It's the derivative of our loss original function, the position function. And then we're gonna differentiate the velocity to get acceleration. No, becomes 12. T square minus 12 T plus two. That's part A For part B. We have We're gonna use our acceleration that we found in part a. Then we're gonna plug in one. When we get two meters perverts stuck in square for part C, we're going to draw a graph so we have our regular function or position function in black. Then I'll look like this. We have our velocity function and red and our acceleration function gangrene