A body starts from rest and moves with constant acceleration... | Physics | SolveeIt

Question

A body starts from rest and moves with constant acceleration for $t \,s$ . It travels a distance $x_1$ in first half of time and $x_2$ in next half of time, then

$x_2=x_1$

$x_2=2x_1$

$x_2=3x_1$

$x_2=4x_1$

Answer

$x_2=3x_1$

Explanation

Solution

We know that $a=\frac{\text { Displacement}}{(\text { Time })^{2}}$
$a=\frac{x_{2}-x_{1}}{t^{2}}$
(if $\left.x_{2}>x_{1}\right)$
By Newton's second law of motion
$s=u t+\frac{1}{2} a t^{2}$
where $u=0$ (body is at rest)
So, $x_{1} =0+\frac{1}{2} \times \frac{x_{2}-x_{1}}{t^{2}} \times t^{2}$
$x_{1} =\frac{x_{2}-x_{1}}{2}$
$\Rightarrow 2 x_{1} =x_{2}-x_{1}$
$3 x_{1} =x_{2}$

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