If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by s(t) = 10t - 1.86t².

The average velocity from t = 1 to t = 2 is
m/s.

The average velocity from t = 1.9 to t = 2 is
m/s.

The average velocity from t = 1.99 to t = 2 is
m/s.

The average velocity from t = 1.999 to t = 2 is
m/s.

From above, it appears that the instantaneous velocity when t = 2 is about
m/s.

(Round to one decimal.)

To solve these problems, we will calculate the average velocity for each given time interval using the formula for average velocity:

\[
\text{Average Velocity} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}
\]

where \( s(t) \) is the height function, and \( t_1 \) and \( t_2 \) are the times.

Given the height function on Mars:
\[
s(t) = 10t - 1.86t^2
\]

### 1. Average Velocity from \( t = 1 \) to \( t = 2 \):

\[
\text{Average Velocity} = \frac{s(2) - s(1)}{2 - 1}
\]

First, calculate \( s(2) \) and \( s(1) \):
\[
s(2) = 10(2) - 1.86(2^2) = 20 - 7.44 = 12.56 \text{ meters}
\]
\[
s(1) = 10(1) - 1.86(1^2) = 10 - 1.86 = 8.14 \text{ meters}
\]
Now, calculate the average velocity:
\[
\text{Average Velocity} = \frac{12.56 - 8.14}{2 - 1} = \frac{4.42}{1} = 4.42 \text{ m/s}
\]

### 2. Average Velocity from \( t = 1.9 \) to \( t = 2 \):

\[
\text{Average Velocity} = \frac{s(2) - s(1.9)}{2 - 1.9}
\]

First, calculate \( s(1.9) \):
\[
s(1.9) = 10(1.9) - 1.86(1.9^2)
\]

Now, compute \( s(1.9) \):
\[
s(1.9) = 19 - 6.72186 = 12.27814 \text{ meters}
\]
Now, calculate the average velocity:
\[
\text{Average Velocity} = \frac{12.56 - 12.27814}{2 - 1.9} = 2.81860 \text{ m/s}
\]

### 3. Average Velocity from \( t = 1.99 \) to \( t = 2 \):

Compute \(s(1.999) \text{ meters}


Explore how to calculate average velocity in kinematics problems using a Mars-based example. This problem involves a rock thrown upward with a given velocity, with calculations spanning various time intervals. Learn the application of quadratic functions and average velocity formulas in physics. Suitable for Grades 10-12.

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