Question

Two trains are moving in the same direction along parallel tracks. One of them is $200 \, m$ long travelling with a velocity of $20 \, m \, s^{- 1}$ . The second one is $800 \, m$ long travelling with a velocity of $7.5 \, m \, s^{- 1}$ . The time taken for the first train to overtake the second is

• A. $20s$
• B. $40s$
• C. $60s$
• D. $80 \, s$

Answer 1

Answer: (D)

From the figure, the relative displacement is

$s_{r e l}=\left(800 + 200\right)m=1000 \, m$
$\left(\upsilon\right)_{r e l}=\left(\upsilon\right)_{1}-\left(\upsilon\right)_{2}=\left(20 - 7.5\right) \, m \, s^{- 1}$
$=12.5 \, m \, s^{- 1}$
$\therefore t=\frac{s_{r e l}}{\upsilon_{r e l}}=\frac{1000}{12.5}=80 \, s$