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The equation of motion of a particle is $ = t^3 - 3t, $ where is in meters and is in seconds. Find(a) the velocity and acceleration as functions of $ t, $(b) the acceleration after $ 2 s, $ and(c) the acceleration when the velocity is 0.

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01:07

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Baylor University

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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The equation of motion of …

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'Ihe motion of a part…

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The acceleration $a$ in $\…

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Given$s(t)=t^{2}-\frac…

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Velocity and Acceleration<…

Hey, it's clear. So in Yuma, read here. So we're going to note that velocity is the derivative of the displacement. He s over DT, which is equal to de over de ti Pretty cute. Minus three T, which is equal to three. T square minus three and we need acceleration. And that's the derivative of velocity. Do you be over DT? That is therefore equal to 60. For part B, we have acceleration, which is equal to 60 to find it. After two seconds, we just have to plug in two for tea that becomes equal to 12 meters per second square. We're seeing we have our velocity equation, which is three t square minus three. We're gonna find out at what time? The velocities zero. So we're gonna plug in zero for B A and Saul for tea. We get T is equal to one. Now we just plug it into acceleration. We get six meters per second square

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