Question Number 191091 by otchereabdullai last updated on 18/Apr/23
$${The}\:{front}\:{of}\:{a}\:{train}\:\mathrm{80}{m}\:{long}\:{passes} \\ $$$${a}\:{signal}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{72}{km}/{h}.\:{If}\:{the} \\ $$$${rear}\:{of}\:{the}\:{train}\:{passes}\:{the}\:{signal}\: \\ $$$$\mathrm{5}{seconds}\:{later},\:{find}\: \\ $$$$\left({a}\right)\:{the}\:{acceleration}\:{of}\:{the}\:{train} \\ $$$$\left({b}\right)\:{the}\:{speed}\:{at}\:{which}\:{the}\:{rear}\:{of}\:{the} \\ $$$${train}\:{passes}\:{the}\:{signal}. \\ $$
Answered by mr W last updated on 18/Apr/23
$${v}_{\mathrm{1}} =\mathrm{72}\:{km}/{h}=\mathrm{20}\:{m}/{s} \\ $$$${s}={v}_{\mathrm{1}} {t}+\frac{{at}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\mathrm{80}=\mathrm{20}×\mathrm{5}+\frac{{a}×\mathrm{5}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\Rightarrow{a}=−\frac{\mathrm{8}}{\mathrm{5}}=−\mathrm{1}.\mathrm{6}\:{m}/{s}^{\mathrm{2}} \\ $$$${v}_{\mathrm{2}} ={v}_{\mathrm{1}} +{at}=\mathrm{20}−\mathrm{1}.\mathrm{6}×\mathrm{5}=\mathrm{12}\:{m}/{s}=\mathrm{43}.\mathrm{2}\:{km}/{s} \\ $$
Commented by otchereabdullai last updated on 18/Apr/23
$${May}\:{Allah}\:{almighty}\:{bless}\:{you} \\ $$