Dynamics continuous motion derivation help

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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