Upchuck Is Slipping!

Calculus Level pending

Ben's one of the awesome alien forms is Upchuck. He can eat up anything and transform those into energy to throw back.

This time Upchuck is at the South Pole. He's standing on a frozen lake, which necessarily indicates frictionless icy surface and he is at rest initially. Vilgax is shooting Upchuck with his destructive Cosmic Rifle. And excess to mention, Upchuck is eating the shots. Consequently, by Newton's third law, Upchuck is slipping backwards. At any time, t(in seconds), you can express Upchuck's displacement(in meters) by this differential equation: \[ds=\frac{At}{B+Ct}dt\] Where, A,B,C are constant. What's Upchuck's displacement(in meters, of course) at \(t=100 seconds\) (Rounded up to the nearest integer)?

Given, \[A=\phi (Golden Ratio)\] \[B=e\] \[C=\pi\]

Bonus: Have you produced the generalized equation for any values of the constant?


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