Cyclist Distance and Velocity Approximations

The video tutorial explains how to calculate the total distance traveled by a cyclist over 12 seconds using velocity data at two-second intervals. It involves plotting a graph of velocity versus time and using right-hand rectangles to approximate the area under the curve, which represents the distance. The tutorial walks through the process of calculating the sum of these areas, known as R of six, and discusses the concept of overestimation and underestimation in this context.

What is the velocity of the cyclist after 4 seconds?

• 9 feet per second

• 10 feet per second

• 7.5 feet per second

• 6 feet per second

What is the velocity of the cyclist at 12 seconds?

• 9.5 feet per second

• 10 feet per second

• 6 feet per second

• 7.5 feet per second

What is the width of each rectangle used in the approximation?

• 2 seconds

• 3 seconds

• 4 seconds

• 1 second

How is the height of a right-hand rectangle determined?

• By the velocity at the end of the interval

• By the average velocity of the interval

• By the velocity at the start of the interval

• By the maximum velocity of the interval

What is the area of the first rectangle in the approximation?

• 16 feet

• 14 feet

• 12 feet

• 10 feet

What is the velocity at the end of the interval for the third rectangle?

• 7.5 feet per second

• 8.5 feet per second

• 9 feet per second

• 9.5 feet per second

What is the total approximate distance traveled by the cyclist?

• 101 feet

• 105 feet

• 95 feet

• 100 feet

Why is the approximation considered an overestimate?

• Because it uses a constant velocity for each interval

• Because it uses the fastest velocity of each interval

• Because it uses the average velocity of each interval

• Because it uses the slowest velocity of each interval

What would a left-hand rectangle approximation result in?

• An overestimate

• An underestimate

• An exact estimate

• A random estimate

What is the purpose of using rectangles in this context?

• To approximate the distance traveled

• To determine the acceleration

• To find the average velocity

• To calculate the exact distance