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The position of an object at any time is given by the equation $s(t)=3 t^{3}-4 t+11 .$ Find the equations of its velocity and acceleration.

$$v=9 t^{2}-4, a=18 t$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Harvey Mudd College

Baylor University

Idaho State 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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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The position of an object …

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The velocity of an object …

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Let $s$ represent the posi…

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An object moves along a co…

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Velocity The position of a…

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Use the given position fun…

question 14 states that the position of an object at any time is given by the equation. S f t equals three t cubed minus 40 plus 11. Uh, then they want you to find the equations of its velocity and acceleration. Ah, for velocity. That's just the derivative of the position equation. Soviet T is equal to nine t squared, minus four. The acceleration is just the derivative of velocity. Therefore, taking the derivative again would just be 18 t and those are your answers for question 14.

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