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How do i prove this, also am i able to assume that coeff friction ≥0?

okay that makes alot more sense, thank you!!

ohh i see what you mean

Sorry let me reword, you cannot do this question using mkv^2, for this question the resistive force would be (mod(sdot))^2 X unit velocity vector, which simplifies into B which is the same as taylors quadratic drag equations -->

There has been 1 question in the hsc that requires the correct model in new syllabus (HSC 2022 4u) Would this not imply that they can test it?

Would i be required to know the correct quadratic drag model for hsc, or is it sufficient to know the one involving mkv^2, (carrotsticks textbook covers the correct drag model but has only 1 question on it).

Why does a surface with resistive force mkv^2 have displacement given by x = 1/k(ln(1+ukt)), hence divering, whereas a surface with resistive force mkv has displacement x = u/k((1-e^-kt)), and converges to x = u/k. Is this because the quadratic drag model is incorrect?