Analyzing the Speed of a Train: A Case Study
In this case study, we will analyze the speed of a train as it travels along a straight track from one station to another. Figure 2.30 shows how the speed of the train varies with time over the whole journey. To determine the time interval over which the train is decelerating, we need to analyze the speed graph. By observing the graph, we can see that the train starts to decelerate after reaching its maximum speed and continues to decelerate until it comes to a stop at the second station. Therefore, the time interval over which the train is decelerating is from the point where the train reaches its maximum speed to the point where it comes to a stop at the second station. Next, we need to determine the acceleration of the train. By observing the speed graph, we can see that the train is constantly decelerating, which means it is experiencing a negative acceleration. Therefore, the acceleration of the train is negative. To determine the distance between the two stations, we can use the formula for distance traveled under constant deceleration. The formula is given by: Distance = (1/2) * initial speed^2 / acceleration By substituting the values from the speed graph into the formula, we can calculate the distance between the two stations. Finally, to determine the average speed of the train over the whole journey, we can use the formula for average speed. The formula is given by: Average speed = total distance / total time By substituting the values we calculated earlier into the formula, we can determine the average speed of the train over the whole journey. In conclusion, by analyzing the speed of a train as it travels along a straight track from one station to another, we can determine the time interval over which the train is decelerating, the acceleration of the train, the distance between the two stations, and the average speed of the train over the whole journey. These calculations provide valuable insights into the dynamics of the train and its journey.