A train starts from rest and reaches a velocity of 100 km/h in 8 minutes. How far does it travel in that time?

To determine how far the train travels while accelerating from rest to a velocity of 100 km/h in 8 minutes, you can use the formula for calculating distance in uniformly accelerated motion. The first step is to convert the velocity from kilometers per hour to meters per second to make the calculations easier.

1. Convert 100 km/h to m/s:

[

100 \text{ km/h} = \frac{100 \times 1000 \text{ m}}{3600 \text{ s}} \approx 27.78 \text{ m/s}

]

2. The time taken is 8 minutes, which can be converted to seconds:

[

8 \text{ minutes} = 8 \times 60 = 480 \text{ seconds}

]

3. Since the train starts from rest, its initial velocity (u) is 0 m/s. The final velocity (v) is 27.78 m/s, and the time (t) is 480 seconds. The average velocity (v_avg) during uniform acceleration can be calculated as:

[

v_{avg} = \frac{u + v}{2} = \frac{0