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A particle moves along a straight line with equation of motion $ s = f(t) $, where $ s $ is measured in meters and $ t $ in seconds. Find the velocity and the speed when $ t = 4 $.

$ f(t) = 10 + \frac{45}{t + 1} $

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04:54

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

David Base G.

October 27, 2020

Finally, now I'm done with my homework

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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Okay, this problem is a position velocity acceleration problem. You're given the position of a particle at twenties, F t is 10 plus 45 over T plus one. The velocity at time T is the derivative of F at time T, Which will be 45 times T plus one to the negative two times a negative. So velocity at four is negative 45 times 5 to the negative, too negative 45/25 which is negative 9/5. The question is written in meters and seconds, so the velocity is in meters per second, acceleration at time T is the derivative of velocity. So that will be positive 90 tons T plus one to the negative three. So acceleration at four is 90 Times 5 to the -3, 90/1, Just 18/25. That will be in leaders per second squared two.

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