Friday, September 4, 1998 Chapter 2 -- Instantaneous Velocity Acceleration Objects in Free Fall Chapter 3 -- Vectors (intro)

When answering questions on the worksheets, be honest! Don’t change your answer based on what I say. Always make a prediction. Don’t worry about being wrong!! Always leave your original prediction. NEVER erase! REMEMBER--your participation in filling out the worksheets is part of a larger effort to improve this class!

clock reading position t1t1 t2t2 Does the velocity of the object = the average velocity for the entire time interval [ t 1, t 2 ]? NO ! Is its velocity less than, equal to, or greater than the average velocity during the time interval [ t 1, t 2 ]? t* At the instant t = t*, object velocity = average velocity For t average velocity For t > t*, object velocity < average velocity

We call the “object velocity,” v, at each instant in time the And we can find the instantaneous velocity of an object by finding the slope of the curve on the position vs. clock reading graph! For what length of time does the instantaneous velocity describe the velocity of an object in motion, such as the one depicted in the graph above? 0 sec !!! clock reading position t1t1 t2t2 t*

clock reading position To better understand and describe the motion of our blue object, we’d like to describe how fast its velocity is changing... Let’s first construct a graph of its velocity versus clock reading using the information in the position vs. clock reading graph. clock reading velocity Sketch this graph on your worksheet. Chat with neighbors!

clock reading velocity This graph provides a useful starting point from which we can determine how fast the velocity is changing. Is this quantity greater than zero, less than zero or equal to zero for out blue object? Is the object speeding up, slowing down, or moving with uniform velocity? tftf titi

clock reading velocity Is this quantity greater than zero, less than zero or equal to zero for out blue object? Is the object speeding up, slowing down, or moving with uniform velocity? What about this one?

“Average acceleration” over the time interval [t i, t f ] Is usually written...

A car accelerates at 2.5 mi/hr/s. Its instantaneous velocity is 20 mi/hr. What will be the velocity of the car at the end of the next second? And the one after that? If the car is accelerates at 2.5 mi/hr/s, then at the end of the next second, the car will be travelling with the velocity = 20 mi/hr mi/hr = 22.5 mi/hr. At the end of the next second the car will be travelling with velocity = 22.5 mi/hr mi/hr = 25 mi/hr.

Is there such thing as an instantaneous acceleration? If so, what does it mean? And why did we decide to use instead of

Galileo chose the left one on a hunch that FREE FALL was uniformly accelerated in the one case but not the other! The progression of science...

Having been through arguments involving instants in time and instantaneous velocity, you can probably guess how to determine the instantaneous acceleration of an object... clock reading velocity Instantaneous Acceleration is given by the slope of the tangent lines. Average Acceleration is given by the slope of the chord.

Please note on your worksheet the meaning of the LENGTH of the line in the following position versus time graphs: clock reading position clock reading position clock reading position Consult with neighbors!

clock reading position clock reading position clock reading position represents a change in position represents a change in time is meaningless WHY? a b [a 2 ] = s 2 [b 2 ] = m 2 a 2 + b 2 = ? a 2 + b 2 = a 2 + b 2