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The equation of motion of a particle is, $ s = 2t^4 - 2t^3 + t^2 - t $ , where is in meters and is inseconds.(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.

00:42

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Boston College

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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

Oregon State University

Harvey Mudd College

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