Question

Two particles one with constant velocity $50m/s$ and the other with uniform acceleration $10m/s^2$, start moving simultaneously from the same place in the same direction. They will be at a distance of $125m$ from each other after

• A. $5sec$
• B. $5(1+\sqrt{2})sec$
• C. $10sec$
• D. $10(\sqrt{2}+1)sec$

Answer 1

The correct option is A $5sec$

$u_1=50m/s$
$u_2=0$
$s_1=u\times t$
$a_2=10m/s^2$
$s_1=50t$
$s_2=u_{2}t+\frac{1}{2}{a}_2{t}^2$
$s_2=0+\frac{1}{2}\times 10\times t^2=5t^2$
$s_1-s_2=125\Rightarrow 50t-5t^2=125$
$\Rightarrow t^2-10t+25=0\Rightarrow t=5$