Question

Two trains start a distance of $2000m$ apart. Train one is moving with a constant speed of $30m/s$ directly towards train $2$ which starts from rest and accelerates with a constant acceleration of $5m/s^2$ directly towards train 1. When do the trains meet?

• A. $22.9s$
• B. $34.9s$
• C. $30s$
• D. $40s$

Answer 1

Answer: (A)

$22.9s$

Let say both trains meet at point P as shown in the figure.
Train 1:
Using $S=ut+\frac{1}{2}a{t}^2$
$\therefore$ $x=0+\frac{1}{2}\left(5\right)t^2$
We get $x=2.5t^2$ .......(1)
Train 2 :
Using $S=ut$
$\therefore$ $2000-x=30t$ .....(2)
Adding (1) and (2), we get
$2000=2.5t^2+30t$
Or $t^2+12t-800=0$
$⟹$ $t=\frac{-12\pm \sqrt{{12}^2-4\left(1\right)(-800)}}{2\times 1}$
Or $t=\frac{-12\pm 57.83}{2\times 1}$
Neglecting the minus sign, $t=\frac{-12+57.83}{2\times 1}=22.9s$