To calculate the total distance covered by the diesel train, we need to consider the three different phases of its motion: acceleration, uniform motion, and deceleration.
- Acceleration phase: The train starts from rest and accelerates uniformly to a speed of 70 km/h in 30 seconds. We can use the formula for uniformly accelerated motion to calculate the distance covered during this phase.
The initial velocity (u) is 0 km/h, the final velocity (v) is 70 km/h, and the time (t) is 30 seconds.
Using the formula: distance = (initial velocity + final velocity) / 2 * time
distance = (0 + 70) / 2 * 30 = 35 * 30 = 1050 meters
Therefore, the distance covered during the acceleration phase is 1050 meters.
- Uniform motion phase: The train continues at a constant speed of 70 km/h for 60 seconds. The distance covered during uniform motion is given by:
distance = speed * time = 70 km/h * 60 seconds
However, the units need to be consistent, so we convert the speed from km/h to m/s:
70 km/h = (70 * 1000) / (60 * 60) m/s = 19.44 m/s
distance = 19.44 m/s * 60 seconds = 1166.4 meters
Therefore, the distance covered during the uniform motion phase is 1166.4 meters.
- Deceleration phase: The train decelerates uniformly from a speed of 70 km/h to rest in 60 seconds. The initial velocity (u) is 70 km/h, the final velocity (v) is 0 km/h, and the time (t) is 60 seconds.
Using the same formula as before:
distance = (initial velocity + final velocity) / 2 * time
distance = (70 + 0) / 2 * 60 = 35 * 60 = 2100 meters
Therefore, the distance covered during the deceleration phase is 2100 meters.
To find the total distance covered, we sum up the distances from all three phases:
Total distance = distance during acceleration + distance during uniform motion + distance during deceleration = 1050 meters + 1166.4 meters + 2100 meters = 4316.4 meters
Therefore, the total distance covered by the diesel train is approximately 4316.4 meters.