Kinematics of Particles Rectilinear Motion Lesson 2 Sections

• Frequently we want to define the motion of the particle by expressing

– Case I: Acceleration given in terms of t. For example: First, look for

So, we start with Note we wrote the acceleration as a(t) to emphasize the

But we want s in terms of t or So we must “transform” v(t)

Look for a fundamental equation that contains v, t, and s © D. J.

So, we start with Then: This gives us s as a function of time

This is what we wanted, s(t) But we already showed that: So: v(t) ©

– Case II: Acceleration given in terms of s. For example: (Problem 2/40) First,

So, we start with Rearranging terms Then This gives us v(s) © D. J.

Thus, we have But we want to get s(t) So we must “transform” v(s)

So, we start with Then: This gives us what we wanted, s as a

– Case III: Acceleration given in terms of v. For example: (Problem 2/40) First,

So, we start with Then This gives us v(t) © D. J. Morrison, 2013

Then as for Case I, once we know v(t) we can find s(t) From

• Special Case: Uniformly accelerated rectilinear motion (UARM) – ACCELERATION is CONSTANT -

Likewise But for UARM So © D. J. Morrison, 2013 17

– For uniformly accelerated rectilinear motion the following equations apply: REMEMBER, UARM MEANS ACCELERATION

Example Problem: L 2 -1 © D. J. Morrison, 2013 20

Example Problem: L 2 -1 Given: so= 3 m Find: s, v, and a,

Example Problem: L 2 -2 © D. J. Morrison, 2013 22

Example Problem: L 2 -2 Given: so= 3 m vo= 10 m/s Find: v(s),

Example Problem: L 2 -3 © D. J. Morrison, 2013 24

Example Problem: L 2 -3 Given: a=1. 5 g = constant so= 0 vo=

Example Problem: L 2 -4 © D. J. Morrison, 2013 26

Example Problem: L 2 -4 Given: a= 0. 4 g = constant vo= 0

Slides: 27

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Kinematics of Particles – Rectilinear Motion Lesson 2 - Sections 2/2 and 2/3 • Rectilinear Motion – Fundamental equations of motion from last class © D. J. Morrison, 2013 1

• Frequently we want to define the motion of the particle by expressing s in terms of t • Consider the following three cases: © D. J. Morrison, 2013 2

– Case I: Acceleration given in terms of t. For example: First, look for a fundamental equation that contains both a and t © D. J. Morrison, 2013 3

So, we start with Note we wrote the acceleration as a(t) to emphasize the fact that a is a function of t. Then: This gives us v as a function of time or v(t) © D. J. Morrison, 2013 4

But we want s in terms of t or So we must “transform” v(t) into s(t) © D. J. Morrison, 2013 5

Look for a fundamental equation that contains v, t, and s © D. J. Morrison, 2013 6

So, we start with Then: This gives us s as a function of time or s(t) © D. J. Morrison, 2013 7

This is what we wanted, s(t) But we already showed that: So: v(t) © D. J. Morrison, 2013 8

– Case II: Acceleration given in terms of s. For example: (Problem 2/40) First, look for a fundamental equation that contains both a and s © D. J. Morrison, 2013 9

So, we start with Rearranging terms Then This gives us v(s) © D. J. Morrison, 2013 10

Thus, we have But we want to get s(t) So we must “transform” v(s) into s(t) Look for a fundamental equation that contains v, t, and s © D. J. Morrison, 2013 11

So, we start with Then: This gives us what we wanted, s as a function of t or s(t) © D. J. Morrison, 2013 12

– Case III: Acceleration given in terms of v. For example: (Problem 2/40) First, look for a fundamental equation that contains both a and v © D. J. Morrison, 2013 13

So, we start with Then This gives us v(t) © D. J. Morrison, 2013 14

Then as for Case I, once we know v(t) we can find s(t) From We already showed that This gives us what we wanted, s as a function of t or s(t) © D. J. Morrison, 2013 15

• Special Case: Uniformly accelerated rectilinear motion (UARM) – ACCELERATION is CONSTANT - not a function of time © D. J. Morrison, 2013 16

– For uniformly accelerated rectilinear motion the following equations apply: REMEMBER, UARM MEANS ACCELERATION IS CONSTANT!!! © D. J. Morrison, 2013 19