Question Number 19828 by NECC last updated on 16/Aug/17
$${The}\:{speed}\:{of}\:{a}\:{train}\:{is}\:{reduced} \\ $$$${from}\:\mathrm{80}{km}/{h}\:{to}\:\mathrm{40}{km}/{h}\:{after} \\ $$$${the}\:{application}\:{of}\:{the}\:{brake}. \\ $$$$\left({i}\right){how}\:{much}\:{further}\:{would}\:{the}\: \\ $$$${train}\:{travel}\:{before}\:{coming}\:{to}\:{rest} \\ $$$$\left({ii}\right){assuming}\:{the}\:{acceleration}\:{is} \\ $$$${kept}\:{constant},{how}\:{long}\:{will}\:{it} \\ $$$${take}\:{to}\:{bring}\:{the}\:{train}\:{to}\:{rest} \\ $$$${after}\:{the}\:{application}\:{of}\:{the}\:{brakes}? \\ $$
Commented by NECC last updated on 16/Aug/17
$${so}\:{sorry}….\:{The}\:{speed}\:{of}\:{a}\:{car}\:{was} \\ $$$${reduced}\:{from}\:\mathrm{80}{km}/{h}\:{to}\:\mathrm{40}{km}/{h} \\ $$$${for}\:\mathrm{500}{m}……. \\ $$$$ \\ $$$${the}\:{other}\:{texts}\:{are}\:{given} \\ $$$$ \\ $$
Answered by Tinkutara last updated on 16/Aug/17
$${v}^{\mathrm{2}} \:−\:{u}^{\mathrm{2}} \:=\:\mathrm{2}{as} \\ $$$${a}\:=\:\frac{\mathrm{40}^{\mathrm{2}} \:−\:\mathrm{80}^{\mathrm{2}} }{\mathrm{2}×\mathrm{0}.\mathrm{5}}\:=\:−\mathrm{4800}\:\mathrm{km}/\mathrm{h}^{\mathrm{2}} \\ $$$$\left({i}\right)\:{s}\:=\:\frac{{v}^{\mathrm{2}} \:−\:{u}^{\mathrm{2}} }{\mathrm{2}{a}}\:=\:\frac{\mathrm{0}\:−\:\mathrm{1600}}{−\mathrm{2}×\mathrm{4800}}\:=\:\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{km} \\ $$$$\mathrm{Means},\:\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{km}\:\mathrm{more}\:\mathrm{after}\:\mathrm{travelling} \\ $$$$\mathrm{500}\:\mathrm{m}\:\mathrm{already}. \\ $$$$\left({ii}\right)\:{t}\:=\:\frac{{v}\:−\:{u}}{{a}}\:=\:\frac{\mathrm{0}\:−\:\mathrm{80}}{−\mathrm{4800}}\:=\:\frac{\mathrm{1}}{\mathrm{60}}\:\mathrm{h}\:=\:\mathrm{1}\:\mathrm{min} \\ $$
Commented by NECC last updated on 16/Aug/17
$${thanks}\:{boss}… \\ $$$${please}\:{do}\:{you}\:{know}\:{any}\:{site}\:{or}\: \\ $$$${pdf}\:{file}\:{that}\:{really}\:{explains}\:{the} \\ $$$${equation}\:{of}\:{motion} \\ $$$$ \\ $$$$ \\ $$