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#1 2021-04-11 12:46:26

mathland
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Registered: 2021-03-25
Posts: 438

Approximating Velocity

An object in rectilinear motion moves according to the equation s = 5 − t^2 (s in centimeters and t in seconds). Approximate the velocity of the object at time
t_0 = 1 by letting t first equal 0.1, then 0.01, and finally 0.001.
What limit does the velocity appear to be approaching?
Organize the results in a table.

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#2 2021-04-11 19:29:34

Bob
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Registered: 2010-06-20
Posts: 9,128

Re: Approximating Velocity

This approach is exactly how differential calculus is developed.

The table will have a row for distance, one for time taken and one for velocity using V = D/T

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2021-04-12 10:29:03

mathland
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Registered: 2021-03-25
Posts: 438

Re: Approximating Velocity

Bob wrote:

This approach is exactly how differential calculus is developed.

The table will have a row for distance, one for time taken and one for velocity using V = D/T

Bob

Can you be more specific? I need you to further explain.

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#4 2021-04-12 20:08:34

Bob
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Registered: 2010-06-20
Posts: 9,128

Re: Approximating Velocity

The top table row starts with the label t and then the values 0.1, 0.01, 0.01 etc.

The second row will have the corresponding Distance (s) values calculated using the formula s = 5 - t^2

The final row will have the V values calculated using V = s / t

What you should observe is values of V getting closer and closer to a limit (the instantaneous velocity at the moment).

This process demonstrates the process known as differentiation from first principles.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2021-04-14 11:57:24

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Approximating Velocity

Bob wrote:

The top table row starts with the label t and then the values 0.1, 0.01, 0.01 etc.

The second row will have the corresponding Distance (s) values calculated using the formula s = 5 - t^2

The final row will have the V values calculated using V = s / t

What you should observe is values of V getting closer and closer to a limit (the instantaneous velocity at the moment).

This process demonstrates the process known as differentiation from first principles.

Bob

Ok. I will work on creating the needed table.

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