Train vs. Bridge: A Classic Relative Motion Problem Solved

A 200-meter train at 60 km/h crosses a bridge in 60 seconds. Find the bridge length. This is a staple physics/math problem—here's the clean solution.

Given

• Train length (L_train) = 200 m
• Speed (v) = 60 km/h = 60 × (1000/3600) = 16.67 m/s = 50/3 m/s
• Time to clear bridge (t) = 1 min = 60 s

Concept

"Passes bridge" = front of train enters bridge → end of train leaves bridge. Distance traveled = bridge length + train length.

Calculation

Distance = v × t = (50/3 m/s) × 60 s = 1000 m

Bridge length = Distance − L_train = 1000 m − 200 m = 800 meters

Verification

• At 50/3 m/s, train covers 200 m (its own length) in 12 s.
• Remaining 48 s × 50/3 m/s = 800 m (bridge).
• Total 60 s ✓

Common Trap

Forgetting to subtract train length → 1000 m (incorrect). The train must move its own length plus the bridge length to fully clear it.

Answer: The bridge is 800 meters long.