To find the speed of the train in kilometers per hour (km/h), we need to follow these steps:
Step 1: Convert the initial acceleration from meters per second squared (m/s²) to kilometers per hour squared (km/h²). 1 m/s² = 3.6 km/h²
So, the acceleration of 0.5 m/s² is equal to (0.5 × 3.6) km/h² = 1.8 km/h².
Step 2: Convert the distance traveled from meters (m) to kilometers (km). 100 m = 0.1 km
Step 3: Use the following kinematic equation to calculate the final speed:
v² = u² + 2as
Where: v = final speed (unknown) u = initial speed (0 since the train starts from rest) a = acceleration (1.8 km/h²) s = distance traveled (0.1 km)
Plugging the values into the equation:
v² = 0² + 2 × 1.8 × 0.1 v² = 0 + 0.36 v = √0.36 v ≈ 0.6 km/h
Therefore, when the train has moved through 100 m, its speed is approximately 0.6 km/h.