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

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

Answer 1

The correct option is A $x_2=3x_1$

$x_1=0+\frac{1}{2}a{\left(\frac{t}{2}\right)}^2=\frac{a{t}^2}{8}$ $[2^{nd}$ equation of motion]

$V_B=0+a\left(\frac{t}{2}\right)=\frac{at}{2}$ $[1^{st}$ equation of motion]

$x_2=\left(\frac{at}{2}\right)\frac{t}{2}+\frac{1}{2}\left(a\right){\left(\frac{t}{2}\right)}^2$

$x_2=\frac{a{t}^2}{4}+\frac{a{t}^2}{8}=\frac{3a{t}^2}{8}$

$⟹x_2=3x_1$