Question Number 4851 by sanusihammed last updated on 17/Mar/16
$${The}\:{distance}\:{moved}\:{by}\:{particle}\:{in}\:{the}\:{sixth}\:{and}\:{eight}\:{seconds} \\ $$$${of}\:{the}\:{motion}\:{are}\:\mathrm{45}{m}\:{and}\:\mathrm{53}{m}\:{repectively}. \\ $$$${Determine}\:{the}\:{acceleration}\:{and}\:{the}\:{initial}\:{speed}. \\ $$
Commented by prakash jain last updated on 18/Mar/16
$$\mathrm{Yes}.\:\mathrm{If}\:\mathrm{motion}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{with}\:\mathrm{uniform} \\ $$$$\mathrm{acceleration}\:\mathrm{is}\:\mathrm{not}\:\mathrm{assumed}\:\mathrm{then}\:\mathrm{the}\:\mathrm{given} \\ $$$$\mathrm{information}\:\mathrm{is}\:\mathrm{not}\:\mathrm{suffcient}. \\ $$
Commented by prakash jain last updated on 17/Mar/16
$$\mathrm{Assuming}\:\mathrm{uniform}\:\mathrm{acceleration} \\ $$$${s}={ut}+\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$$$\mathrm{Distance}\:\mathrm{travelled}\:\mathrm{in}\:{n}^{{th}} \:\mathrm{second} \\ $$$${s}_{{n}} ={un}+\frac{\mathrm{1}}{\mathrm{2}}{an}^{\mathrm{2}} −\left({u}\left({n}−\mathrm{1}\right)+\frac{\mathrm{1}}{\mathrm{2}}{a}\left({n}−\mathrm{1}\right)^{\mathrm{2}} \right) \\ $$$${s}_{{n}} ={u}+\frac{\mathrm{1}}{\mathrm{2}}{a}\left({n}^{\mathrm{2}} −\left({n}−\mathrm{1}\right)^{\mathrm{2}} \right) \\ $$$${s}_{{n}} ={u}+\frac{\mathrm{1}}{\mathrm{2}}{a}\left(\mathrm{2}{n}−\mathrm{1}\right) \\ $$$$\mathrm{45}={u}+\frac{\mathrm{13}}{\mathrm{2}}{a} \\ $$$$\mathrm{53}={u}+\frac{\mathrm{15}}{\mathrm{2}}{a} \\ $$$${a}=\mathrm{8} \\ $$$${u}=−\mathrm{7} \\ $$$$−{ve}\:{value}\:{of}\:{u}\:{indicate}\:{that}\:{initial}\:{velcotiy} \\ $$$${and}\:{acceration}\:{are}\:{in}\:{different}\:{direction}. \\ $$
Commented by Yozzii last updated on 17/Mar/16
$${What}\:{if}\:{the}\:{body}\:{does}\:{not}\:{move}\:{along} \\ $$$${a}\:{straight}\:{line}\:{or}\:{its}\:{acceleration}\:{is} \\ $$$${variable}? \\ $$
Commented by prakash jain last updated on 17/Mar/16
$$\mathrm{Assuming}\:\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{and} \\ $$$$\mathrm{motion}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}. \\ $$$$\mathrm{Taking}\:\mathrm{question}\:\mathrm{as}\:\mathrm{initial}\:\mathrm{topics}\:\mathrm{on}\:\mathrm{kinematics}. \\ $$
Commented by Yozzii last updated on 17/Mar/16
$${Otherwise},\:{there}'{s}\:{insufficient} \\ $$$${information}\:{to}\:{obtain}\:{a}\:{general} \\ $$$${answer}? \\ $$