Question

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

• A. $x_2=x_1$
• B. $x_2=2x_1$
• C. $x_2=3x_1$
• D. $x_2=4x_1$

Answer 1

Answer: (C)

We know that $a=\frac{Displacement}{{\left(Time\right)}^2}$
$a=\frac{x_2-x_1}{t^2}\left(if{x}_2>x_1\right)$
by Newton's second law of motion
$s=ut+\frac{1}{2}a{t}^2$
Where u = 0 (Body is at rest)
So, $x_1=0+\frac{1}{2}\times \frac{x_2-x_1}{t^2}\times t^2$
$x_1=\frac{x_2-x_1}{2}$
$\Rightarrow 2x_1=x_2-x_1$
$3x_1=x_2$