1. Tardigrade
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  4. A particle moves with uniform acceleration along a straight line AB. Its velocities at A and B are 2 m/s and 14 m/s, respectively. M is the mid-point of AB. The particle takes t1 seconds to go from A to M and t2 seconds to go from M to B. Then t2/t1 is

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Q. A particle moves with uniform acceleration along a straight line $AB$. Its velocities at $A$ and $B$ are $2 \,m/s$ and $14 \,m/s$, respectively. $M$ is the mid-point of $AB$. The particle takes $t_{1}$ seconds to go from $A$ to $M$ and $t_{2}$ seconds to go from $M$ to $B$. Then $t_{2}/t_{1}$ is

Motion in a Straight Line

Solution:

$v^{2}=2^{2}+\frac{2as}{2}$
image
$\Rightarrow v^{2}-4=as \, \dots (i)$
$14^{2}-v^{2}=\frac{2as}{2}$
$\Rightarrow 196-v^{2}=as \, \dots (ii)$
From (i) and (ii),
$v^{2}-4=196-v^{2}$
$\Rightarrow v=10\,m/s$
Now $t_{1}=\frac{v-2}{a}=\frac{10-2}{a}=\frac{8}{a}$
$t_{2}=\frac{14-v}{a}=\frac{14-10}{a}=\frac{4}{a}$
$\Rightarrow \frac{t_{2}}{t_{1}}=\frac{4/a}{8/a}=\frac{1}{2}$