Question

1. a train starts from rest and speeds up for 15 minutes until it reaches a constant velocity of 100 miles/hour. it stays at this speed for half an hour. then it slows down for another 15 minutes until it is still. which of the following correctly describes the position vs time graph of the trains journey? a. the first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave downward curve. b. the first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave upward curve. c. the first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope zero, and the last portion is a concave downward curve. d. the first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope zero, and the last portion is a concave upward curve.

Explanation:

Step1: Analyze the first - 15 minutes

The train starts from rest and speeds up. In a position - time graph, the velocity is the slope of the graph. When the train is accelerating (speeding up from rest), the slope of the position - time graph is increasing. A curve that has an increasing slope is concave upward.

Step2: Analyze the middle portion

The train is moving at a constant velocity of 100 miles/hour. In a position - time graph, a constant velocity means a straight - line graph, and the slope of the line is equal to the velocity. So the slope of the line for this part is 100 miles/hour.

Step3: Analyze the last 15 minutes

The train is slowing down until it stops. The slope of the position - time graph is decreasing. A curve with a decreasing slope is concave downward.

Answer:

A. The first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave downward curve.