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S18 PH 121 2 intro

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by

Richard Datwyler

on 14 January 2019

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Transcript of S18 PH 121 2 intro

What is a dimension?
What is the derivative of Sine (2t)

A. -2 sine (2t)
B. -2 cosine (2t)
C. 2 sine (2t)
D. 2 cosine (2t)

What is the Derivative of
A bicycles position-vs-time graph is shown below
What is the bicyclist's velocity at t = 10 s, 25 s, & 35 s?
TIME = 10 s

A. -10 m/s
B. -2.5 m/s
C. 0 m/s
D. 2.5 m/s
E. 10 m/s
TIME = 25 s

A. -10 m/s
B. -2.5 m/s
C. 0 m/s
D. 2.5 m/s
E. 10 m/s
TIME = 35 s

A. -10 m/s
B. -2.5 m/s
C. 0 m/s
D. 2.5 m/s
E. 10 m/s
Constant Acceleration:

any examples?

All of what we will do with motion
will have constant acceleration
(rare exceptions will be stated)

Example what can we do with this? (acceleration)
Now this equation takes the form of:
From the definition of acceleration
we have DERIVED an equation for Velocity.

Yeah, but I thought we already had an equation for velocity?
So what is the difference between them
and when would you use them?
In a similar manner we can derive all sorts of kinematics.
Your book does just fine, let me know if you want to go through it, you can come see me later.
Let us rather collect the main three equations of motion
Velocity (no time)
Velocity
Position
Collect the three:
To use these equations I need:

A. Initial position
B. Initial velocity
C. Acceleration
D. Time
E. Some / All : Depends
To solve for 2 (final position) directly
I only need:
1. initial position 2. final position
3. inital velocity 4. final velocity
5. acceleration 6. time

A. 1, 3, & 5
B. 1, 3, & 4
C. 1, 3, 4, & 5
What is Free Fall?
"Can you explain more in depth about derivatives and how they are used?"
"I think I have a good grasp on what instantaneous velocity is, but I get lost while trying to understand how to find the instantaneous velocity. Could you go over this in class?"
INSTANTANEOUS VELOCITY?!!!???!!!
"I know this isn't a calculus class, but can you cover derivatives? "
"I'm having trouble interpreting the velocity and acceleration vs time graphs"
"Can you help me to understand how to find the area under a curve?"
Calculus review
derivative : change in one quantity , while something else is changing
so for velocity...
(while the time changes, how does the______change?

Idea of a limit
we can measure two different positions (and thus calculate displacement)
But it takes time
as the time gets smaller we do better at getting the Instantaneous velocity
Full transcript