/*! 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 81 Solve. \(s=v_{i} t+\frac{1}{2}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 81

Solve. \(s=v_{i} t+\frac{1}{2} a t^{2},\) for \(a\) (a physics formula)

Short Answer

Expert verified
The solution for 'a' is \( a = \frac{2(s - v_i t)}{t^2} \).

Step by step solution

01

Write down the original equation

Start with the given equation: \[ s = v_i t + \frac{1}{2} a t^2 \]
02

Isolate the term containing 'a'

Subtract the initial velocity term (\(v_i t\)) from both sides of the equation to isolate the term with 'a': \[ s - v_i t = \frac{1}{2} a t^2 \]
03

Multiply both sides by 2

To get rid of the fraction, multiply both sides of the equation by 2: \[ 2(s - v_i t) = a t^2 \] This simplifies to: \[ 2s - 2v_i t = a t^2 \]
04

Solve for 'a'

Finally, divide both sides of the equation by \(t^2\) to solve for 'a': \[ a = \frac{2(s - v_i t)}{t^2} \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving for a variable
Solving for a variable means figuring out its value by making it the subject of the equation. In this exercise, we need to solve for 'a' in the physics equation.
We start with the equation: \( s = v_{i} t + \frac{1}{2} a t^{2} \)
Our target is to isolate 'a' so we can find out its value in terms of 's', 'v_i', and 't'.
This process involves several algebraic manipulation steps, which we'll cover next.
isolation of terms
Isolation of terms is a crucial step in solving equations. Here, we need to isolate the term containing 'a' to get closer to our goal.
First, we subtract the term involving initial velocity (\(v_i t\)) from both sides, to leave only the term with 'a' on one side: \( s - v_i t = \frac{1}{2} a t^2 \)
This step ensures we're focusing on the part of the equation that includes 'a', simplifying our calculations.
algebraic manipulation
Algebraic manipulation refers to the rearrangement and simplification of equations using algebraic rules.
To eliminate the fraction, we multiply both sides of our isolated equation by 2: \( 2(s - v_i t) = a t^2 \)
This step transforms our equation to: \( 2s - 2v_i t = a t^2 \)
Finally, we divide by \(t^2\) to solve for 'a': \( a = \frac{2(s - v_i t)}{t^2} \)
Algebraic manipulation helps in simplifying complex expressions into manageable steps.
physics formula
Physics formulas relate different physical quantities and help us understand how they interact.
In this problem, the equation represents the motion of an object. Each term has a specific meaning:
  • \(s\): position
  • \(v_i\): initial velocity
  • \(t\): time
  • \(a\): acceleration
By solving for one variable, we can determine its value based on the other known values.
Physics formulas are powerful tools that enable us to predict and understand various phenomena.

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

Write a problem for a classmate to solve for which fractions must be multiplied in order to get the answer.

Convert to scientific notation. 0.0000013

Chess Ratings. The formula $$R=r+\frac{400(W-L)}{N}$$ is used to establish a chess player's rating \(R,\) after he or she has played \(N\) games, where \(W\) is the number of wins, \(L\) is the number of losses, and \(r\) is the average rating of the opponents. Ulana's rating is 1305 after winning 5 games and losing 3 games in tournament play. What was the average rating of her opponents? (Assume that there were no draws.)

Use set-builder notation to write each set. The set of all multiples of 5 between 7 and 79

Simplify. Assume that all variables represent nonzero integers. $$ \frac{25 x^{a+b} y^{b-a}}{-5 x^{a-b} y^{b+a}} $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.