14.2 Resistive forces - low speed case

[@markbrightwell3536]

From a strictly mathematical point of view, absolute values are indeed needed when you integrate the left hand side (at 5:38). First you evaluate the anti derivative at the limits to get the form ln|A| - ln|B|. Simplify to get ln(|A|/|B|), and then ln|A/B|. Then because both A and B are negative, their ratio is positive. Thus, you can drop the absolute values.

[@legomasterbuilder9118]

I have a physics C test tomorrow about this content. This is helping a lot!

[@telescopilan]

Why can we skip putting an absolute value inside the ln when integrating 1 / x?

[@tech_science_tutos4155]

why we treat acceleration as velocity derivative?

[@talibeilm21c]

Because acceleration is time-derivative of the velocity function. That is how acceleration is defined.

[@tech_science_tutos4155]

@@talibeilm21c why he didn't use y double dot

[@talibeilm21c]

@@tech_science_tutos4155 y double dot is a representation of the double derivative of y which is same as derivative of velocity i.e. acceleration.

[@talibeilm21c]

@@tech_science_tutos4155 Also on one side of the equation we already had v so it was feasible to break "a" into dv/dt.