the height in feet of a flare t seconds after it is shot is modeled by h(t)= -16t2+92t+3.5 find its average speed from 1 to 3 seconds

To do that, divide the distance traveled by the time elapsed.

h(1) = 79.5
h(3) = 135.5

so, avg speed is 56ft/2s = 28ft/s

he height in feet of a flare t seconds after it is shot is modeled by h(t)= -16t2+92t+3.5 find its average speed from 2 to 5 seconds

Great.!!

Well, let's find the average speed of the flare from 1 to 3 seconds!

To find the average speed, we need to calculate the total distance traveled and divide it by the total time taken.

First, let's find the distance traveled by finding the difference in height between t = 1 and t = 3 seconds:

h(1) = -16(1)² + 92(1) + 3.5 = 79.5 feet
h(3) = -16(3)² + 92(3) + 3.5 = 187.5 feet

The distance traveled is the difference: 187.5 - 79.5 = 108 feet.

Now, let's calculate the total time taken: 3 - 1 = 2 seconds.

Finally, to find the average speed, we divide the total distance traveled by the total time taken:

Average speed = Distance / Time = 108 feet / 2 seconds = 54 feet/second.

So, the average speed of the flare from 1 to 3 seconds is 54 feet per second. That's quite a speedy flare!

To find the average speed of the flare from 1 to 3 seconds, we need to calculate the total distance traveled by the flare during that time interval and then divide it by the time taken.

The average speed is given by the formula:

Average Speed = Total Distance / Time

To calculate the total distance traveled by the flare from 1 to 3 seconds, we need to find the displacement (change in height) of the flare at both 1 and 3 seconds.

At 1 second:
h(1) = -16(1)^2 + 92(1) + 3.5 = 79.5 feet

At 3 seconds:
h(3) = -16(3)^2 + 92(3) + 3.5 = 140.5 feet

The total distance traveled by the flare from 1 to 3 seconds is the absolute difference between the heights at these two times:

Total Distance = |h(3) - h(1)| = |140.5 - 79.5| = 61 feet

Now, we can calculate the average speed:

Average Speed = Total Distance / Time = 61 / (3 - 1) = 61 / 2 = 30.5 feet per second

Therefore, the average speed of the flare from 1 to 3 seconds is 30.5 feet per second.