/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 90 Given the following acceleration... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 90

Given the following acceleration functions of an object moving along a line, find the position function with the given initial velocity and position. $$a(t)=4 ; v(0)=-3, s(0)=2$$

Short Answer

Expert verified
Question: Determine the position function, s(t), of an object moving along a straight line, given its acceleration function a(t) = 4, initial velocity v(0) = -3, and initial position s(0) = 2. Answer: The position function of the object is $$s(t)=2t^2 - 3t + 2$$.

Step by step solution

01

Find the Velocity Function (integration of Acceleration Function)

Given the acceleration function, we can find the velocity function by integrating the acceleration function with respect to time "t". The given acceleration function is $$a(t)=4$$ Integrating it with respect to time, we get: $$v(t) = \int 4 dt = 4t+C$$
02

Determine the Constant "C" using Initial Velocity

We are given the initial velocity, $$v(0)=-3$$. Now, we use this information to determine the constant "C": $$-3=4(0) + C$$ From this equation, we get the value of C as $$C = -3$$ Next, we substitute this value into the velocity function: $$v(t)=4t - 3$$
03

Find the Position Function (integration of Velocity Function)

To find the position function s(t), we need to integrate the velocity function with respect to time "t", obtained in Step 2: $$s(t) = \int (4t - 3) dt = 2t^2 - 3t + D$$
04

Determine the Constant "D" using Initial Position

We are given the initial position, $$s(0)=2$$. Now, we use this information to determine the constant "D" as follows: $$2 = 2(0)^2 - 3(0) + D$$ From this equation, we get the value of D as $$D = 2$$ Next, we substitute this value into the position function: $$s(t)=2t^2 - 3t + 2$$ Now we have found the position function of the object moving along a line as $$s(t)=2t^2 - 3t + 2$$

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider the general cubic polynomial \(f(x)=x^{3}+a x^{2}+b x+c,\) where \(a, b,\) and \(c\) are real numbers. a. Show that \(f\) has exactly one inflection point and it occurs at \(x^{*}=-a / 3\) b. Show that \(f\) is an odd function with respect to the inflection point \(\left(x^{*}, f\left(x^{*}\right)\right) .\) This means that \(f\left(x^{*}\right)-f\left(x^{*}+x\right)=\) \(f\left(x^{*}-x\right)-f\left(x^{*}\right),\) for all \(x\)

Given the following acceleration functions of an object moving along a line, find the position function with the given initial velocity and position. $$a(t)=2 \cos t ; v(0)=1, s(0)=0$$

Verify the following indefinite integrals by differentiation. $$\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x=2 \sin \sqrt{x}+C$$

Find the function \(F\) that satisfies the following differential equations and initial conditions. $$F^{\prime \prime}(x)=\cos x, F^{\prime}(0)=3, F(\pi)=4$$

Find the function \(F\) that satisfies the following differential equations and initial conditions. $$F^{\prime \prime}(x)=1, F^{\prime}(0)=3, F(0)=4$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.