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mathland

Member

Registered: 2021-03-25

Posts: 444

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

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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

mathland

Member

Registered: 2021-03-25

Posts: 444

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

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

mathland

Member

Registered: 2021-03-25

Posts: 444

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

Ok. I will work on creating the needed table.