A train is 150 meters long. It overtakes a person walking in the same direction at a speed of 2 km/h in 3 seconds. Find the speed of the train.

Given:

• Length of train = 150 m
• Speed of person = 2 km/h
• Time taken to overtake = 3 s

Step 1: Convert speed of person to m/s

$2 \text{ km/h} = \frac{2 \times 1000}{3600} = \frac{5}{9} \text{ m/s}$

Step 2: Let speed of train = $v$ m/s

Relative speed (same direction):
$v - \frac{5}{9}$

Step 3: Use formula

Distance = Speed × Time$150 = \left(v - \frac{5}{9}\right) \times 3$

Step 4: Solve

Divide both sides by 3:
$50 = v - \frac{5}{9}$$v = 50 + \frac{5}{9}$
$v = \frac{450 + 5}{9} = \frac{455}{9}$ m/s

Step 5: Convert to km/h

$v = \frac{455}{9} \times \frac{18}{5}$Cancel:
$= 455 \times \frac{2}{5} = 182$ km/h

Final Answer: 182 km/h