Question

A body starts from rest and moves with constant acceleration for $tsec$. It travels a distance $x_1$ in first half of time and $x_2$ in 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)

$x_2=3x_1$

A body starts from rest and moves with constant acceleration a (say) for $tsec$.
$x_1$ distance covered in first half of time.
$\therefore$
$$x_1=\frac{1}{2}a\frac{t^2}{4}$$
At end of $\frac{t}{2}$ s, velocity
$$v=a\frac{t}{2}$$

$x_2$ distance covered in second half of time
$$x_2=v\frac{t}{2}+\frac{1}{2}a\frac{t^2}{4}$$Putting value of $v$ in the equation
$$x_2=a\frac{t^2}{4}+\frac{1}{2}a\frac{t^2}{4}$$

$$x_2=\frac{3}{2}a\frac{t^2}{4}=3x_1$$