The train is 110 m long. Speed of the train ($v_t$) = 58 kmph. Speed of the passerby ($v_p$) = 4 kmph. They are moving in the same direction. When objects move in the same direction, their relative speed is the difference between their speeds. Relative speed ($v_{rel}$) = $v_t - v_p = 58 \text{ kmph} - 4 \text{ kmph} = 54 \text{ kmph}$. To pass the passerby, the train needs to cover a distance equal to its own length relative to the passerby. Distance to be covered = Length of the train = 110 m. We need to convert the relative speed from kmph to m/s. 1 kmph = 1000 meters / 3600 seconds = 5/18 m/s. $v_{rel} = 54 \text{ kmph} = 54 \times \frac{5}{18} \text{ m/s} = 3 \times 5 \text{ m/s} = 15 \text{ m/s}$. Time taken = Distance / Relative speed. Time = 110 m / 15 m/s. Time = $\frac{110}{15}$ seconds. Simplify the fraction: $\frac{110}{15} = \frac{22 \times 5}{3 \times 5} = \frac{22}{3}$ seconds. Convert the improper fraction to a mixed number: $\frac{22}{3} = 7$ with a remainder of 1, so $7 \frac{1}{3}$ seconds.
A train 110 m long is travelling at a speed of 58 kmph. The time in which it will pass a passerby walking at 4 kmph in the same direction is
Asked in BPSC Prelims Exam 67th Cancelled · Topic: Mechanics (Newton's Laws of Motion and their applications)
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