To find the speed of the train in kilometers per hour (km/h) when it has moved through 100 meters, we can use the following steps:
Convert the distance from meters to kilometers: Distance = 100 m = 100/1000 km = 0.1 km
Use the equation of motion to find the final velocity of the train: v^2 = u^2 + 2as
Where: v = final velocity (unknown) u = initial velocity (which is 0 m/s since the train starts from rest) a = acceleration = 0.5 m/s^2 s = distance = 0.1 km
Substituting the given values into the equation, we have: v^2 = 0^2 + 2 * 0.5 * 0.1
v^2 = 0 + 0.1
v^2 = 0.1
Taking the square root of both sides to solve for v: v = √0.1
v ≈ 0.316 m/s
- Convert the final velocity from meters per second (m/s) to kilometers per hour (km/h): v (in km/h) = v (in m/s) * 3.6
v (in km/h) = 0.316 m/s * 3.6
v (in km/h) ≈ 1.138 km/h
Therefore, when the train has moved through 100 meters, its speed is approximately 1.138 km/h.