Question

a train 200 m long is moving at 11 m/s and completely passes a man running in the same direction on the platform in 20 s. what is the speed of the man?
a 8 m/s
b 3 m/s
c 4 m/s
d 1 m/s

Explanation:

Step1: Calculate relative - speed distance relationship

The train passes the man completely. The distance covered is the length of the train, $d = 200$ m, and the time taken is $t = 20$ s. The relative - speed $v_{rel}$ of the train with respect to the man is given by the formula $v_{rel}=\frac{d}{t}$.
$v_{rel}=\frac{200}{20}=10$ m/s.

Step2: Find the man's speed

The speed of the train $v_{train}=11$ m/s. Since the man and the train are moving in the same direction, $v_{rel}=v_{train}-v_{man}$. Then $v_{man}=v_{train}-v_{rel}$.
$v_{man}=11 - 10=1$ m/s.

Answer:

d. $1$ m/s