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2 Exercise: Go through the algebra to show that the above leads to

2 Exercise: Go through the algebra to show that the above leads to

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Trying to figure out how to prove the exercise on the bottom of the page.

We usually write this in the form 1 (v²(1) - v² (0)] + (0). 31,and bus suis 2a This equation, which of course holds only for constant acceleration since it comes from our handy equations for the special case, and at t₁ we have be very useful. Before going to examples lets show first that our three equations for the special case so much of constant acceleration can be put in yet another form which does not depend on when we started our clock or where we called a = 0. For example at t = 12 we hau v(t₂) = at₂ + v(0) v²(t)- v²(0) = 2a [z(t)-(0)]. Or Subtracting the second from the first gives and subtracting, v(t₁) = at₁ +v(0). 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(t₂) - v(t₁)= a(t₂-t₁) z(t₂) = z(t₁) = at² +v(0)t₂ + x(0) 2 1 at² +v(0)t₁ + 2(0) 2 1 x(t₂) - x(t₁) == a. (t²-1²)+v(0) (t₂-t₁) 2 Exercise: Go through the algebra to show that the above leads to noape brooss sel 1 - z(t₂) — z(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁). 2
Transcribed Image Text:We usually write this in the form 1 (v²(1) - v² (0)] + (0). 31,and bus suis 2a This equation, which of course holds only for constant acceleration since it comes from our handy equations for the special case, and at t₁ we have be very useful. Before going to examples lets show first that our three equations for the special case so much of constant acceleration can be put in yet another form which does not depend on when we started our clock or where we called a = 0. For example at t = 12 we hau v(t₂) = at₂ + v(0) v²(t)- v²(0) = 2a [z(t)-(0)]. Or Subtracting the second from the first gives and subtracting, v(t₁) = at₁ +v(0). 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(t₂) - v(t₁)= a(t₂-t₁) z(t₂) = z(t₁) = at² +v(0)t₂ + x(0) 2 1 at² +v(0)t₁ + 2(0) 2 1 x(t₂) - x(t₁) == a. (t²-1²)+v(0) (t₂-t₁) 2 Exercise: Go through the algebra to show that the above leads to noape brooss sel 1 - z(t₂) — z(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁). 2
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