Two trains each of length 100m are running on two parallel trucks .One train overtakes the other in 20s and one train crosses the other in 10s. Calculate the velocity of each train

The velocity of one of the trains is 15 m/s

The velocity of the other train 5 m/s

Explanation:

The given parameters of the two trains and the motion of the trains are;

The length of each train, l = 100 m

The time it takes one train to overtake the other, Δt₁ = 20 s

The time it takes the one train to cross the other, Δt₂ = 10 s

Let 'v₁' represent the velocity of one of the trains, and let 'v₂' represent the velocity of the other train, we have;

When one train overtakes the other, the trains are moving in the same direction and the relative velocity of the overtaking train, v = v₁ - v₂

The distance the train travels when overtaking or crossing, d = 2 × l

∴ d = 2 × 100 m = 200 m

d = 200 m

Therefore, we get;

v = v₁ - v₂ = d/Δt₁ = (200 m)/(20 s) = 10 m/s

∴ v₁ - v₂ = 10 m/s                                        Equation (1)

When one train crosses the other train, the trains are moving in opposite directions on the different tracks, therefore, we have;

For the overtaking trains, v = v₁ + v₂ = d/Δt₂ = (200 m)/(10 s) = 20 m/s

∴ v₁ + v₂ = 20 m/s                                        Equation (2)

Adding equation (1) to equation (2) gives;

v₁ - v₂ + v₁ + v₂ = 2·v₁ = 10 m/s + 20 m/s = 30 m/s

∴ v₁ = 30 m/s/2 = 15 m/s

The velocity of one of the trains, v₁ = 15 m/s

From equation (2), we  have;

v₁ + v₂ = 20 m/s

v₂ = 20 m/s - v₁

∴ v₂ = 20m/s - 15 m/s = 5 m/s

The velocity of the other train, v₂ = 5 m/s.

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