Problem 52 Easy Difficulty

Solve the given problems by finding the appropriate derivatives.
The force $F$ (in $\mathrm{N}$ ) on an object is $F=12 d v / d t+2.0 v+5.0$ where $v$ is the velocity (in $\mathrm{m} / \mathrm{s}$ ) and $t$ is the time (in s). If the displacement is $s=25 t^{0.60},$ find $F$ for $t=3.5 \mathrm{s}.$

Answer

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Basic Technical Mathematics with Calculus

Chapter 23

The Derivative

Section 9

Higher Derivatives

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Problem 52

Video Transcript

Okay, four point for number twenty two. Again, we're asked to take the derivative of a fraction. If we look over here, I have my little way of remembering the quotient rule to help out. And the low is the bottom of the fraction it's in blue guys. The top of the fraction it's in green D means to take the derivative So low. D high is low times derivative of the top function. So using this little device here and going to find the derivative we have that y prime is equal to low. So that's just writing the bottom so low. Twelve wass fry Oops, twelve plus five key to the negative point five t low d high. So the derivative of five hundred five hundred is a constant, so the derivative is going to be zero. So this should just be times zero minus Hi, five hundred three, right? That's what's a little bit nicer minus five hundred de lo, which is the derivative of the bottom. If we go over here the derivative of twelve zero, then we have five e to the negative point five t. So that's an exponential, the derivative of an exponential is the exponential right now e to the negative point five t times the derivative of the top, which in this case, is negative point. Fine. And if we go back to the new moniker that is all over so divided by all over the square of what's below, which is twelve plus five. Yeah, to the negative point fi t. Okay, And now we conduce. Um, simplification. Zero times. Anything is zero. So this whole first can is going to go away. It's going to go to zero. So then we're just left with negative five hundred times, five times negative, point five. And if we cuddle that together, the negative and the negative were going to cancel. You have five times, five hundred times, point five. I'm gonna let you guys work on that simplification one thousand two hundred and fifty e to the negative point five t and the bottom stays the same. We're not going to make any changes to the bottom twelve plus five e to the negative point. Sy t. This right here is going to be the final answer. So, to recap, we have low bottom function derivative of the top of the fraction, which was zero minus the top of the fraction five hundred times the derivative of the low, which is the derivative of the bottom. So we're taking the derivative of the bottom. This right here is an exponential is your exponential function. So we have five e negative point five tea. And to find this derivative, you had to bring down the native point five, which is the derivative of the exponents which has seen right here as well. Again, this is your final answer something.

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Basic Technical Mathematics with Calculus

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Problem 52 Easy Difficulty

Solve the given problems by finding the appropriate derivatives.
The force $F$ (in $\mathrm{N}$ ) on an object is $F=12 d v / d t+2.0 v+5.0$ where $v$ is the velocity (in $\mathrm{m} / \mathrm{s}$ ) and $t$ is the time (in s). If the displacement is $s=25 t^{0.60},$ find $F$ for $t=3.5 \mathrm{s}.$

Answer

Related Courses

Basic Technical Mathematics with Calculus

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Functions on the Real Line - Overview

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Watch More Solved Questions in Chapter 23

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Kayleah T.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Basic Technical Mathematics with Calculus

Grace H.

Kayleah T.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Kayleah T.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus