Question

A bus and car are stopped next to each other at a light. When the light turns green they start at the same time. Let t be the number of seconds since the light turned green. (a) The distance (in meters) the car has driven since the light turned green is given by c=t² +2t. What is the car's average speed between t=2 and t=5 seconds?

Answer 1

The car's average speed between t=2 and t=5 seconds is calculated by finding the total distance traveled using the equation c=t² + 2t and dividing by the time interval. The result is 9 meters per second.

Step-by-step explanation:

To calculate the car's average speed between t=2 and t=5 seconds, we need to find the total distance traveled over that time interval and then divide by the duration of the interval. The distance the car has traveled since the light turned green is given by the equation c=t² + 2t. Using this equation, we calculate the distance at t=2 and t=5:

• At t=2 seconds: c=2² + 2(2) = 4 + 4 = 8 meters
• At t=5 seconds: c=5² + 2(5) = 25 + 10 = 35 meters

To find the distance traveled between these times, we subtract the distance at t=2 from the distance at t=5:

Distance traveled from t=2 to t=5 is 35 meters - 8 meters = 27 meters.

The time interval is 5 seconds - 2 seconds = 3 seconds.

Therefore, the average speed is distance / time interval = 27 meters / 3 seconds = 9 meters per second.