How do I calculate instantaneous velocity?

AI Thread Summary
To calculate instantaneous velocity, you need to find the derivative of the position function. For the given function F(T) = 5T^3 - 2T^2 - 48, the derivative is F'(T) = 15T^2 - 4T. To find the instantaneous velocity at T = 12 seconds, substitute 12 into the derivative, resulting in F'(12) = 15(12)^2 - 4(12). The derivative represents the slope of the tangent line, indicating the instantaneous rate of change at that specific point in time. Understanding this concept is crucial for applying instantaneous velocity in various contexts.
Michael17
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Can anyone please explain to me how to work out instantaneous velocity. I do not understand it and how to apply it. Any help would be greatly appriciated.

thank you.
 
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If the position of an insect is given by the equation F(T) = 5T3 - 2T2 - 48 and you want to find the instantaneous velocity at a particular point T = 12 seconds, you must solve for F'(12).

That is, you take the derivative of F(T), which in this case is F'(T) = 15T2 - 4T
and then you get F'(12) = 15(12)2 - 4(12)

The derivative is the slope of the tangent line so it represents the instantaneous rate of change at a particular point.
 
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Thank you very much.
 
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