over a time interval of 2.27 years, the velocity of a planet orbiting a distant star reverses direction, changing from +18.3km/s to -22.0km/s. Find the total change in the planet's velocity in m/s and its average acceleration in m/s^2 in this time interval



### 1. Total Change in Velocity (in m/s):

The total change in the planet's velocity (\(\Delta v\)) is the difference between its final velocity and initial velocity. The velocities are given as:

- Initial velocity (\(v_i\)) = +18.3 km/s
- Final velocity (\(v_f\)) = -22.0 km/s

Since the velocities are given in km/s, we'll convert them to m/s:

\[
v_i = 18.3 \, \text{km/s} = 18.3 \times 1000 \, \text{m/s} = 18300 \, \text{m/s}
\]
\[
v_f = -22.0 \, \text{km/s} = -22.0 \times 1000 \, \text{m/s} = -22000 \, \text{m/s}
\]

Now, we calculate the change in velocity:

\[
\Delta v = v_f - v_i = (-22000 \, \text{m/s}) - (18300 \, \text{m/s})
\]
\[
\Delta v = -22000 - 18300 = -40300 \, \text{m/s}
\]

So, the total change in velocity is **-40,300 m/s**.

### 2. Average Acceleration (in m/s²):

The average acceleration (\(a_{\text{avg}}\)) is calculated using the formula:

\[
a_{\text{avg}} = \frac{\Delta v}{\Delta t}
\]

Where:
- \(\Delta v = -40300 \, \text{m/s}\) (from the previous step),
- \(\Delta t = 2.27 \, \text{years} = 2.27 \times 365 \times 24 \times 3600 \, \text{seconds}\).

Let's convert the time interval to seconds and compute the average acceleration.

\[
\Delta t = 2.27 \times 365 \times 24 \times 3600 \, \text{seconds} = 71673120 \, \text{seconds}
\]

Now, calculate the average acceleration:

\[
a_{\text{avg}} = \frac{-40300 \, \text{m/s}}{71673120 \, \text{s}} \approx -5.62 \times 10^{-4} \, \text{m/s}^2
\]

### Final Answers:
1. Total change in velocity: **-40,300 m/s**
2. Average acceleration: **-5.62 × 10⁻⁴ m/s²**

Would you like more details on any step?

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Here are 5 related questions to extend your understanding:
1. How do velocity changes affect the orbit of planets?
2. What other methods can be used to measure the velocity of planets?
3. How does average acceleration differ from instantaneous acceleration?
4. What role does gravity play in reversing the direction of a planet's velocity?
5. How can we calculate orbital parameters from velocity and acceleration?

**Tip**: Always convert time intervals to seconds in physics problems unless otherwise stated.

Over a time interval of 2.27 years, the velocity of a planet orbiting a distant star reverses direction, changing from +18.3km/s to -22.0km/s. Find the total change in the planet's velocity in m/s and its average acceleration in m/s^2 in this time interval.

Explore how to calculate the total change in velocity and average acceleration of a planet that reverses direction over a 2.27-year interval. This problem covers key kinematic concepts like velocity change, acceleration, and unit conversion. Suitable for high school students in Grades 11-12.

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