Question

The Graph shows the velocity of a train

a) use four strips of equal width to estimate the distance the train travelled in the first 20 seconds
b) is your answer to part a) an understimate or an overestimate?

Answer 1

To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:

a) Calculate the average velocity for each strip by finding the average height of each strip.

b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.

c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.

Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.

Without seeing the graph, it's difficult to provide a definitive answer.

Answer 2

The train travelled 500 meters in the first 20 seconds. This is an overestimate of the actual distance.

The velocity of the train is given in the graph. We can estimate the distance traveled in the first 20 seconds by using four strips of equal width.

| Strip | Time Interval (seconds) | Average Velocity (meters/second) | Area (square meters) |

| 1 | 0-5 | 10 | 50 |

| 2 | 5-10 | 30 | 150 |

| 3 | 10-15 | 35 | 175 |

| 4 | 15-20 | 25 | 125 |

The total area of the four strips is 500 square meters. Since 1 meter of distance is equal to 1 square meter of area when graphed with velocity on the y-axis and time on the x-axis, we can estimate that the train traveled 500 meters in the first 20 seconds.

This is an overestimate of the actual distance traveled. This is because the velocity is not constant throughout the time interval. The velocity is actually increasing from 0 to 20 meters per second during the first 5 seconds, and then decreasing from 20 to 0 meters per second during the next 15 seconds. As a result, the four strips of equal width overestimate the actual area under the curve.

A more accurate estimate of the distance traveled could be obtained by using a larger number of strips with smaller widths.