Question Number 48187 by Rio Michael last updated on 20/Nov/18
$$\mathrm{The}\:\mathrm{data}\:\mathrm{arranged}\:\mathrm{below}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{table}\:\mathrm{was}\:\mathrm{obtained} \\ $$$$\mathrm{for}\:\mathrm{a}\:\mathrm{motor}\:\mathrm{cyclist}\:\mathrm{of}\:\mathrm{total}\:\mathrm{mass}\:\mathrm{120}{kg}\:{traveling}\:{from}\: \\ $$$${Sun}\:{city}\:{towards}\:{Delta}\:{state}. \\ $$$$ \\ $$$${velocity}/{ms}^{−\mathrm{1}} \:\:\mathrm{00}\:\:\:\:\:\mathrm{20}\:\:\:\:\:\mathrm{40}\:\:\:\mathrm{50}\:\:\:\:\:\mathrm{50}\:\:\:\:\mathrm{60}\:\:\:\mathrm{70}\:\:\:\:\mathrm{85} \\ $$$$\:\:\:\:\:{time},{t}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{00}\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:\:\mathrm{10}\:\:\:\:\mathrm{12}\:\:\:\:\:\mathrm{20}\:\:\:\mathrm{35}\:\:\:\:\mathrm{40}\:\:\:\:\mathrm{45} \\ $$$$\left.{i}\right)\:{plot}\:{a}\:{graph}\:{of}\:{velocity}\left({y}−{axis}\right)\:{against}\:{time}\left({x}−{axis}\right) \\ $$$$\left.{ii}\right)\:{Detemine}\:{the}\:{acceleration}\:{of}\:{the}\:{cyclist}\:{for}\:{the}\:{first}\:{part}\:{of}\:{the}\:{motion} \\ $$$$\left.{iii}\right)\:{Calculate}\:{the}\:{pull}\:{of}\:{the}\:{engine}\:{during}\:{the}\:{first}\:\mathrm{12}.\mathrm{5}{s} \\ $$$${if}\:{this}\:{section}\:{of}\:{the}\:{road}\:{is}\:{horizontal}\:{and}\:{friction}\:{with}\:{all} \\ $$$${other}\:{forces}\:{is}\:{negligible}. \\ $$$$\left.{iv}\right){what}\:{is}\:{the}\:{momentum}\:{change}\:{during}\:{the}\:{first}\:\mathrm{12}.\mathrm{5}^{{th}} \:{second} \\ $$$$\left.{v}\right)\:{detemine}\:{the}\:{kinetic}\:{energy}\:{of}\:{the}\:{cyclist}\:{at}\:{the}\:\mathrm{37}.\mathrm{5}^{{th}} \:{second} \\ $$$$\left.{vi}\right)\:{for}\:{how}\:{long}\:{is}\:{the}\:{resultant}\:{force}\:{zero}\:{on}\:{the}\:{cyclist} \\ $$$${during}\:{motion}? \\ $$