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 $a=\frac{D i s p l a c e m e n t}{\left(T i m e\right)^{2}}$
$a=\frac{x_{2} - x_{1}}{t^{2}} \, \, \left(i f \, x_{2} > x_{1}\right)$
by Newton's second law of motion
$s=ut+\frac{1}{2}at^{2}$
Where u = 0 (Body is at rest)
So, $x_{1}=0+\frac{1}{2}\times \frac{x_{2} - x_{1}}{t^{2}}\times t^{2}$
$x_{1}=\frac{x_{2} - x_{1}}{2}$
$\Rightarrow 2x_{1}=x_{2}-x_{1}$
$3x_{1}=x_{2}$