Find an expression in terms of S1 and S2 for the magnitude of the resistance force

Question: https://prnt.sc/rerhdk
My working out: https://prnt.sc/rftqja
Answer in textbook: https://prnt.sc/reroyg


I've been stuck on this Q for hours, the closest form I could get to the solution in the textbook is by using a d-t graph which gives me the speed instead of RF: https://prnt.sc/rfvsj7

Well your distance time graph is going to be incorrect; we have constant deceleration, so velocity will be linear (a straight line), but displacement will be a curve (part of a quadratic in shape).

Your velocity time graph wants to start at a positive value and descend in a straight line. If it started at zero, there would be no resistive force as there's no motion.

You seem to assume that Sn is the distance travelled in the first n seconds. It's not, it's the distance travelled in the n^th second, i.e. from time, t=n-1 to t=n.

PS: Agree with their answer.

I still get the wrong answer: www.prnt.sc/rgphs4

You want to do S1-Sn, rather than S1+Sn, in order to eliminate the u.

Thanks. But even with the u, isn’t it technically correct? The question didn’t ask me to simplify my answer.