Help for Dynamics Continuous Motion

AI Thread Summary
The discussion focuses on obtaining a specific figure related to continuous motion in dynamics. A user seeks clarification on integrating the function (0.8t + A)^{-1/2} and learns that neglecting the constant 0.8 during integration was the mistake. Another participant explains how to evaluate the integral at specific limits, emphasizing the importance of subtracting the evaluated values. The user acknowledges their error in evaluation, realizing that evaluating at zero resulted in zero. The conversation highlights common pitfalls in integration and the importance of careful evaluation.
JamieShumJr
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Can someone tell me how to obtain the figure in red circle? I've trying out on my own but can't get that.
 

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Welcome to PF!

Hi JamieShumJr! Welcome to PF! :smile:
JamieShumJr said:
Can someone tell me how to obtain the figure in red circle? I've trying out on my own but can't get that.

You're asking why is ∫ (0.8t + A)-1/2 dt = (2/0.8)(0.8t + A)1/2 …

apply the https://www.physicsforums.com/library.php?do=view_item&itemid=353" twice …

if you differentiate the RHS, you get an extra 0.8 from the t, and an extra 1/2 from the power, = (0.8/2) :wink:
 
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tiny-tim said:
Hi JamieShumJr! Welcome to PF! :smile:


You're asking why is ∫ (0.8t + A)-1/2 dt = (2/0.8)(0.8t + A)1/2 …

apply the https://www.physicsforums.com/library.php?do=view_item&itemid=353" twice …

if you differentiate the RHS, you get an extra 0.8 from the t, and an extra 1/2 from the power, = (0.8/2) :wink:

Thanks a lot!:smile: I neglected the 0.8 during the integration. Got it already. Forgotten the basic rule of integration. :frown:
 
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may i know from same question as above shown, how to get the -1/60 at the end there?
 
welcome to pf!

hi mintz! welcome to pf! :smile:
mintz said:
may i know from same question as above shown, how to get the -1/60 at the end there?

the ##|^t_0## at the end of the previous line means you have to evaluate it at t and at 0, and subtract :wink:
 
tiny-tim said:
hi mintz! welcome to pf! :smile:


the ##|^t_0## at the end of the previous line means you have to evaluate it at t and at 0, and subtract :wink:

oh~okie~thanks! i made mistake that evaluate at 0 whole things became 0~:frown:
thanks anyway!=D
 

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