If a rock is thrown upward on the planet Mars with a velocity of 13 m/s, its height in meters t seconds later is given by y = 13t − 1.86t2. (Round your answers to two decimal places.)

(a) Find the average velocity over the given time intervals.

To find the average velocity over a given time interval, we need to calculate the change in position (height) over that time interval and divide it by the duration of the interval.

Let's consider two time intervals:

Interval 1: From t = 0 to t = 2 seconds
Interval 2: From t = 0 to t = 5 seconds

For interval 1, we need to calculate the change in position (Δy) from t = 0 to t = 2 seconds:

Δy = y(2) - y(0)
= (13(2) - 1.86(2)^2) - (13(0) - 1.86(0)^2)
= 26 - 7.44 - 0
= 18.56 meters

The duration of interval 1 is 2 seconds. Therefore, the average velocity (v1) over this interval is:

v1 = Δy / Δt
= 18.56 / 2
= 9.28 m/s (rounded to two decimal places)

For interval 2, we need to calculate the change in position (Δy) from t = 0 to t = 5 seconds:

Δy = y(5) - y(0)
= (13(5) - 1.86(5)^2) - (13(0) - 1.86(0)^2)
= 65 - 46.5 - 0
= 18.5 meters

The duration of interval 2 is 5 seconds. Therefore, the average velocity (v2) over this interval is:

v2 = Δy / Δt
= 18.5 / 5
= 3.70 m/s (rounded to two decimal places)

So, the average velocity over the given time intervals is 9.28 m/s for the first 2 seconds and 3.70 m/s for the first 5 seconds.

To find the average velocity over a given time interval, you need to calculate the displacement divided by the time interval. In this case, the formula for the displacement is given by the equation y=13t−1.86t^2.

For the given time interval, you need to find the displacement at the beginning and the end of this interval. Then, you can calculate the average velocity.

Let's say the initial time is t1 and the final time is t2. The displacement at time t1 is y1=13t1−1.86t1^2, and the displacement at time t2 is y2=13t2−1.86t2^2.

The average velocity can be calculated using the following formula:
Average Velocity = (Displacement)/(Time Interval)

Time Interval = t2 - t1

Using this information, you can now plug in the values to calculate the average velocity.

Take the code from the Master..

the interval [a,b]

(((13*b)-(1.86*b^2))-((13*a)-(1.86*a^2)))/b-a

make b smaller and smaller until you reach the correct instantaneous velocity