Homework Help is Here – Start Your Trial Now!
Science
Physics
comes from our This equation, which of of constant acceleration can be put in yet another form which does not depend so much Before going to examples lets show first that our three equations for the special case on when we started our clock or where we called x = 0. For example at t = t2 we have handy equations for the special case, will be very useful. v(t₂) = at₂ + v(0) or and at t₁ we have Subtracting the second from the first gives and subtracting, v(t₂) - v(t₁)= a (t₂-1₁) v(t₂) = a (t₂-t₁) +v(t₁). This really says the same thing as the original equation: The velocity at the end of a time interval is the velocity at the beginning plus the acceleration times the time interval. Doing the same thing for the second equation we have v(t₁) = at₁ +v(0). 1 x(t₂) = at +v(0)t₂ + x(0) x(t₁) = = (t₂) - (t₁) = at +v(0)t₁ + x(0) 1 2a. (t – tỉ) + n(0)(tz - t) Exercise: Go through the algebra to show that the above leads to 1 x(t₂) − x(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁). HINT: You have to use v(t₁) = at₁ +v(0). (This equation also has the same interpretation as the original equation if one considers time intervals.) Exercise: Show that the third formula, relating the values of v², leads to v² (1₂) - v² (t₁) = 2a [x(t₂) - (t₁)]. 1

comes from our This equation, which of of constant acceleration can be put in yet another form which does not depend so much Before going to examples lets show first that our three equations for the special case on when we started our clock or where we called x = 0. For example at t = t2 we have handy equations for the special case, will be very useful. v(t₂) = at₂ + v(0) or and at t₁ we have Subtracting the second from the first gives and subtracting, v(t₂) - v(t₁)= a (t₂-1₁) v(t₂) = a (t₂-t₁) +v(t₁). This really says the same thing as the original equation: The velocity at the end of a time interval is the velocity at the beginning plus the acceleration times the time interval. Doing the same thing for the second equation we have v(t₁) = at₁ +v(0). 1 x(t₂) = at +v(0)t₂ + x(0) x(t₁) = = (t₂) - (t₁) = at +v(0)t₁ + x(0) 1 2a. (t – tỉ) + n(0)(tz - t) Exercise: Go through the algebra to show that the above leads to 1 x(t₂) − x(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁). HINT: You have to use v(t₁) = at₁ +v(0). (This equation also has the same interpretation as the original equation if one considers time intervals.) Exercise: Show that the third formula, relating the values of v², leads to v² (1₂) - v² (t₁) = 2a [x(t₂) - (t₁)]. 1

Glencoe Physics: Principles and Problems, Student Edition
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter2: Representing Motion
Section: Chapter Questions
Problem 69A
See similar textbooks
icon
Related questions
icon
Concept explainers
Topic Video
Question
100%

On the excercise in the image, I am unable to figure out how to solve these algebraically.

This equation, which of cou handy equations for the special case, will be very useful. comes from c of constant acceleration can be put in yet another form which does not depend Before going to examples lets show first that our three equations for the special on when we started our clock or where we called x = 0. For example at t = t2 we have v(t₂) = at₂ + v(0) or and at t₁ we have Subtracting the second from the first gives and subtracting, v(t₂) - v(t₁) = a (t₂ - 1₁) v(t₁) = at₁ +v(0). v(t₂) = a (t₂-t₁) +v(t₁). interval is the velocity at the beginning plus the acceleration times the time interval. Doing the same thing for the second equation we have This really says the same thing as the original equation: The velocity at the end of a time x (t₂) = z(t₁) = x(t₂) - x(t₁) = 1 at +v(0)t₂ + x(0) at² + v(0)t₁ + x(0) 1 · 2 x(1₂) − x(t₁) = a (t²- t²) + v(0)(t₂ − t₁) - Exercise: Go through the algebra to show that the above leads to noitsups broosa edT case 17 a a. (t₂-t₁)² + v(t₁)(t2 — t₁). 2 as the original equation if one considers time intervals.) HINT: You have to use v(t₁) = at₁ +v(0). (This equation also has the same interpretation Exercise: Show that the third formula, relating the values of v², leads to v²(t₂) - v²(t₁) = 2a[r(t₂) - x(t₁)]. 22 st i
Transcribed Image Text:This equation, which of cou handy equations for the special case, will be very useful. comes from c of constant acceleration can be put in yet another form which does not depend Before going to examples lets show first that our three equations for the special on when we started our clock or where we called x = 0. For example at t = t2 we have v(t₂) = at₂ + v(0) or and at t₁ we have Subtracting the second from the first gives and subtracting, v(t₂) - v(t₁) = a (t₂ - 1₁) v(t₁) = at₁ +v(0). v(t₂) = a (t₂-t₁) +v(t₁). interval is the velocity at the beginning plus the acceleration times the time interval. Doing the same thing for the second equation we have This really says the same thing as the original equation: The velocity at the end of a time x (t₂) = z(t₁) = x(t₂) - x(t₁) = 1 at +v(0)t₂ + x(0) at² + v(0)t₁ + x(0) 1 · 2 x(1₂) − x(t₁) = a (t²- t²) + v(0)(t₂ − t₁) - Exercise: Go through the algebra to show that the above leads to noitsups broosa edT case 17 a a. (t₂-t₁)² + v(t₁)(t2 — t₁). 2 as the original equation if one considers time intervals.) HINT: You have to use v(t₁) = at₁ +v(0). (This equation also has the same interpretation Exercise: Show that the third formula, relating the values of v², leads to v²(t₂) - v²(t₁) = 2a[r(t₂) - x(t₁)]. 22 st i
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Displacement, velocity and acceleration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Glencoe Physics: Principles and Problems, Student…
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
University Physics Volume 1
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
SEE MORE TEXTBOOKS