91Ó°ÊÓ

Change in velocity is an important concept in physics that describes how the speed and direction of an object, such as a planet, shifts over time. In this exercise, we observe a planet's velocity transitioning from \( +20.9 \, \mathrm{km/s} \) to \( -18.5 \, \mathrm{km/s} \).
This involves not just a change of speed, but also a reversal in direction. The formula used to calculate the change in velocity \( \Delta v \) is:

• \( \Delta v = v_f - v_i \)

where \( v_f \) is the final velocity and \( v_i \) is the initial velocity.
This calculation helps determine how quickly the planet is decelerating or accelerating in the opposite direction. Here, substituting the given velocities:

• \( \Delta v = -18,500 \,\mathrm{m/s} - 20,900 \,\mathrm{m/s} = -39,400 \,\mathrm{m/s} \)

The negative sign indicates not only a slow down but also a change in direction to the opposite.

Converting velocity values from one unit to another is crucial, as it ensures consistency in measurements, especially in scientific calculations. In this context, converting from kilometers per second (km/s) to meters per second (m/s) involves a straightforward multiplication:

• 1 kilometer = 1000 meters

To convert the initial planet's velocity from \( +20.9 \, \mathrm{km/s} \) to meters per second, multiply by 1000:

• \( 20.9 \,\mathrm{km/s} \times 1000 = 20,900 \,\mathrm{m/s} \)

Similarly, for the final velocity \( -18.5 \, \mathrm{km/s} \):

• \( -18.5 \,\mathrm{km/s} \times 1000 = -18,500 \,\mathrm{m/s} \)

Ensuring your units are consistent allows you to accurately compare and calculate changes in physical quantities.

Accurately converting time units is a fundamental step when working with extended periods. Here, the time interval given is in years, which must be converted to seconds to properly compute average acceleration.
One year is typically approximated to contain:

• 365.25 days (accounting for leap years)
• Each day has 24 hours
• Each hour has 60 minutes
• Each minute has 60 seconds

To convert 2.16 years into seconds:

• \( 2.16 \,\text{years} \times 31,557,600 \, \text{seconds/year} = 68,162,976 \, \text{seconds} \)

This conversion is essential for accurately determining rates of change, such as acceleration, over time.

Planetary motion refers to the movement of planets, often around a star, and involves complex interactions of forces, primarily gravity.
In this particular exercise, examining the velocity change of a planet helps us understand the dynamics of its orbit.Average acceleration in this context shows how the planet's speed and direction systematically change. The formula for average acceleration \( a_{avg} \) is:

• \( a_{avg} = \frac{\Delta v}{\Delta t} \)

where \( \Delta v = -39,400 \,\mathrm{m/s} \) and time interval \( \Delta t = 68,162,976 \, \text{seconds} \).
Calculating gives:

• \( a_{avg} = \frac{-39,400}{68,162,976} \approx -5.78 \times 10^{-4} \,\mathrm{m/s^2} \)

This negative acceleration indicates the reversal direction of the planet's motion. Understanding these concepts aids in studying the nature of celestial bodies and their movements in the universe.