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Kinetic energy is a way to measure an object's energy based on its motion. The formula used to calculate the kinetic energy \( KE \) of an object is \( KE = \frac{1}{2} mv^2 \), where \( m \) represents the mass in kilograms and \( v \) is the velocity in meters per second.
In the case of the asteroid, we start by calculating its initial and final kinetic energy. Initially, the velocity \( v_i \) is 7100 m/s, which means we need to substitute this into the formula along with the mass \( 4.5 \times 10^4 \) kg. This calculation provides us with the initial kinetic energy:
\[ KE_i = \frac{1}{2} \times 4.5 \times 10^4 \times 7100^2. \]
For the final kinetic energy, we use the final velocity \( v_f \) of 5500 m/s in a similar manner:
\[ KE_f = \frac{1}{2} \times 4.5 \times 10^4 \times 5500^2. \]
The difference between these two energy values tells us about the work done by the force in changing the asteroid's energy state.

Force calculations often begin with the concept of work done, which in physics is a way to quantify the energy transferred when an object is moved over a distance by a force. Here, the work done \( W \) is found using the change in kinetic energy. Using the work-energy principle, we know
\[ W = KE_f - KE_i. \]
This principle states that the total work done on an object is equal to the change in its kinetic energy.
Once we've determined the work \( W \), we can find the force \( F \) applied using the formula
\[ W = F \cdot d, \]
where \( d \) is the distance over which the force is applied, which is given as \( 1.8 \times 10^6 \) m in this asteroid scenario. Rearranging the formula as
\[ F = \frac{W}{d}, \]
allows us to solve for the magnitude of the force. This gives us a clear understanding of how much force is required to slow the asteroid over the specified distance.

Asteroids are fascinating celestial objects orbiting around the sun, mostly found in the asteroid belt between Mars and Jupiter. Understanding their motion is crucial for navigational and collision avoidance studies.
In this exercise, the asteroid's motion through space is influenced by a force that alters its speed. Initially, the asteroid was moving at 7100 m/s, and due to the applied force, slows down to 5500 m/s. This change in motion implies the asteroid is experiencing a deceleration.
Such deceleration (slowing down) might be due to gravitational pulls from nearby planets, or possibly due to impacts with other space debris. The change in speed over a particular distance (1.8 million meters in this case) gives us key insights into the forces acting upon it.
Knowing how to calculate these changes in motion is crucial in the broader study of asteroids, particularly when planning missions to potentially redirect their paths or understanding their origins and compositions.