Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as a function of time as the trains slow down. What is the separation between the trains (in metre) when both have stopped?

Question

Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as a function of time as the trains slow down. What is the separation between the trains (in metre) when both have stopped? Question

(A) (B) (C) (D)

Tardigrade Admin · Accepted Answer

Using the concept that the area under the

v - t

graph gives the change in displacement.

s_{1} = \frac{1}{2} \times 10 \times 40 = 200 m

s_{2} = \frac{- 1}{2} \times 8 \times 20 = - 80 m

Relative displacement

(s)_{relative} = s_{1} - s_{2} = (200) - (- 80) = 280

Final separation

= 300 - 280 = 20 m

Using the concept that the area under the v−t graph gives the change in displacement. s1​=21​×10×40=200m s2​=2−1​×8×20=−80m Relative displacement (s)relative​=s1​−s2​=(200)−(−80)=280 Final separation =300−280=20m