If a train starts from rest and reaches a velocity of 100km/h in 8 minutes, how far will it travel?

To determine the distance traveled by the train, we begin by converting the speed from kilometers per hour to kilometers per minute since the time is given in minutes. The train reaches a velocity of 100 km/h, which can be converted as follows:

100 km/h = 100 km/60 min ≈ 1.67 km/min.

Next, we find the time in minutes that the train travels. Since it accelerates from rest to this speed in 8 minutes, we can use the average speed over this duration to calculate the distance traveled. Since the train starts from rest, the average speed during the acceleration phase can be calculated as half of the final speed, because it is uniformly accelerating:

Average speed = (0 + 1.67 km/min) / 2 = 0.835 km/min.

Now, we can determine the total distance traveled by multiplying the average speed by the time:

Distance = Average speed × Time

Distance = 0.835 km/min × 8 min = 6.68 km.

Rounding this to two decimal places gives us 6.67 km. This is why the answer A, 6.67 km, is correct. It accurately reflects the distance covered given the conditions specified in