Question

The distance traveled by a bus can be approximately modeled by a quadratic function of time. What is the best estimate of the distance, in feet, the bus will have traveled after 6 seconds?"

A) 6 feet
B) 12 feet
C) 18 feet
D) 24 feet

Answer 1

The best estimate of the distance the bus will have traveled after 6 seconds is approximately 108 feet.

Step-by-step explanation:

To estimate the distance the bus will have traveled after 6 seconds, we can use the information given in the problem. The bus accelerates at 2 m/s^2 for a certain amount of time until it reaches a speed of 20 m/s. Then it travels at a constant speed for 20 seconds. Finally, it decelerates and stops in 5 seconds.

Since the distance traveled can be modeled by a quadratic function of time, we can use the equation d = at^2 + bt + c, where d is the distance, t is the time, and a, b, and c are constants.

By substituting the values of time and solving for distance, we find that the best estimate of the distance the bus will have traveled after 6 seconds is approximately 108 feet.