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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 45m and 53m repectively. Determine the acceleration and the initial speed.

$${The}\:{distance}\:{moved}\:{by}\:{particle}\:{in}\:{the}\:{sixth}\:{and}\:{eight}\:{seconds} \\ $$$${of}\:{the}\:{motion}\:{are}\:\mathrm{45}{m}\:{and}\:\mathrm{53}{m}\:{repectively}. \\ $$$${Determine}\:{the}\:{acceleration}\:{and}\:{the}\:{initial}\:{speed}. \\ $$

Commented by prakash jain last updated on 18/Mar/16

Yes. If motion in a straight line with uniform acceleration is not assumed then the given information is not suffcient.

$$\mathrm{Yes}.\:\mathrm{If}\:\mathrm{motion}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{with}\:\mathrm{uniform} \\ $$$$\mathrm{acceleration}\:\mathrm{is}\:\mathrm{not}\:\mathrm{assumed}\:\mathrm{then}\:\mathrm{the}\:\mathrm{given} \\ $$$$\mathrm{information}\:\mathrm{is}\:\mathrm{not}\:\mathrm{suffcient}. \\ $$

Commented by prakash jain last updated on 17/Mar/16

Assuming uniform acceleration s=ut+(1/2)at^2 Distance travelled in n^(th) second s_n =un+(1/2)an^2 −(u(n−1)+(1/2)a(n−1)^2 ) s_n =u+(1/2)a(n^2 −(n−1)^2 ) s_n =u+(1/2)a(2n−1) 45=u+((13)/2)a 53=u+((15)/2)a a=8 u=−7 −ve value of u indicate that initial velcotiy and acceration are in different direction.

$$\mathrm{Assuming}\:\mathrm{uniform}\:\mathrm{acceleration} \\ $$$${s}={ut}+\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$$$\mathrm{Distance}\:\mathrm{travelled}\:\mathrm{in}\:{n}^{{th}} \:\mathrm{second} \\ $$$${s}_{{n}} ={un}+\frac{\mathrm{1}}{\mathrm{2}}{an}^{\mathrm{2}} −\left({u}\left({n}−\mathrm{1}\right)+\frac{\mathrm{1}}{\mathrm{2}}{a}\left({n}−\mathrm{1}\right)^{\mathrm{2}} \right) \\ $$$${s}_{{n}} ={u}+\frac{\mathrm{1}}{\mathrm{2}}{a}\left({n}^{\mathrm{2}} −\left({n}−\mathrm{1}\right)^{\mathrm{2}} \right) \\ $$$${s}_{{n}} ={u}+\frac{\mathrm{1}}{\mathrm{2}}{a}\left(\mathrm{2}{n}−\mathrm{1}\right) \\ $$$$\mathrm{45}={u}+\frac{\mathrm{13}}{\mathrm{2}}{a} \\ $$$$\mathrm{53}={u}+\frac{\mathrm{15}}{\mathrm{2}}{a} \\ $$$${a}=\mathrm{8} \\ $$$${u}=−\mathrm{7} \\ $$$$−{ve}\:{value}\:{of}\:{u}\:{indicate}\:{that}\:{initial}\:{velcotiy} \\ $$$${and}\:{acceration}\:{are}\:{in}\:{different}\:{direction}. \\ $$

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?

$${What}\:{if}\:{the}\:{body}\:{does}\:{not}\:{move}\:{along} \\ $$$${a}\:{straight}\:{line}\:{or}\:{its}\:{acceleration}\:{is} \\ $$$${variable}? \\ $$

Commented by prakash jain last updated on 17/Mar/16

Assuming uniform acceleration and motion in a straight line. Taking question as initial topics on kinematics.

$$\mathrm{Assuming}\:\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{and} \\ $$$$\mathrm{motion}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}. \\ $$$$\mathrm{Taking}\:\mathrm{question}\:\mathrm{as}\:\mathrm{initial}\:\mathrm{topics}\:\mathrm{on}\:\mathrm{kinematics}. \\ $$

Commented by Yozzii last updated on 17/Mar/16

Otherwise, there′s insufficient information to obtain a general answer?

$${Otherwise},\:{there}'{s}\:{insufficient} \\ $$$${information}\:{to}\:{obtain}\:{a}\:{general} \\ $$$${answer}? \\ $$

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