# motion in a straight line

Solution 1

Solution 2 Need to find $a_2$/$a_1$. But I am getting different answers. I found out there can be more solutions other than these two. I am confused why this is happening? Plz Help.

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A particle is moving on a straight line with u (m$s^-1$) initial velocity and it will stop after traveling d distance(m) during T seconds. The deceleration for the motion is $a_1$.(m$s^-2$) Another particle is moving on the same straight line with nu (m$s^-1$) initial velocity and it will stop after traveling d distance(m) during T seconds. The deceleration for the motion is $a_2$.(m$s^-2$). Find the ratio of $a_2$/$a_1$

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A few words explaining what in blazes those diagrams are supposed to mean would also be welcome. –  Gerry Myerson Jun 28 '12 at 13:28
It would seem that one of your equations is inaccurate. I am not sure which. It would either be $v^2=u^2+2as$ or $v=u+at.$ Your ratios make sense, assuming that you are trying to find $n$. –  000 Jun 28 '12 at 13:41
no want to find the ratio. –  Sara Jun 28 '12 at 13:52

You problem is absurd.It can't happen that two bodies with different velocities stop with same stopping distance and in same time given uniform decelerations.Your result is just the proof of my statement($n^2=n\implies n=1$($0$ excluded)).

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if $a_1$ < $a_2$ it can happen right??? I don't know. plz can you explain more. With a simple example. plz. –  Sara Jun 28 '12 at 15:28
i said whatever uniform decelerations you take,it can't happen.Your problem is my example.decelerations need to be non-uniform. –  Aang Jun 28 '12 at 15:33

Data provided in this question is redundant. According to the question we know four variable.

Initial velocity $u$

Final velocity $v = 0$

Distance travelled $d$

Time taken to traverse the distance $T$

And in addition to the above we know that the acceleration is uniform.Given this condition we can determine the acceleration with any three of above four variables. For example you showed $2$ ways in your solutions. In first solution $T$ was ignored and in second $d$ was ignored. You can find other two by disregarding $u$ initial velocity and $v$ final velocity.

So, in short the data is redundant.

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