91Ó°ÊÓ

Understanding "change in velocity" is crucial when analyzing the motion of an object before and after an event, like a collision. In our example, a hand striking a target in tae-kwon-do illustrates this concept.The initial velocity \( v_i \) is the speed at which the hand moves towards the target. Here, it is given as \(13 \mathrm{~m/s}\). When the hand stops, the final velocity \( v_f \) becomes \(0 \mathrm{~m/s}\). Thus, the **change in velocity** \( \Delta v \) can be found using:\[ \Delta v = v_f - v_i = 0 - 13 = -13 \mathrm{~m/s} \]This negative sign indicates a decrease in speed. It tells us that the hand is stopping, rather than accelerating forward. This change is vital for calculating other quantities, such as impulse and force, which depend on how drastically the velocity changes.

In the context of momentum and impulse, **average force** helps us understand how a force acts over a certain period. It tells us about the constant force that could cause the observed changes in motion, like accelerating or stopping a moving object.From the impulse-momentum theorem, we know:\[ J = F_{avg} \cdot \Delta t \]where \(J\) is impulse and \(\Delta t\) is the time duration of contact.In our tae-kwon-do example, the impulse is \(-9.1 \mathrm{~N} \cdot \mathrm{s}\), and the contact time is \(5.5 \mathrm{~ms}\), converted to \(0.0055 \mathrm{~s}\). This allows us to calculate the average force:\[ F_{avg} = \frac{J}{\Delta t} = \frac{-9.1 \mathrm{~N} \cdot \mathrm{s}}{0.0055 \mathrm{~s}} \approx -1654.5 \mathrm{~N} \]The magnitude of the average force is \(1654.5 \mathrm{~N}\). Understanding average force gives insight into how much force is exerted during the short time the hand is in contact with the target.

**Collision duration** refers to the time period over which a collision takes place. It is notably brief when fast-moving objects suddenly come to a stop, like in our tae-kwon-do scenario.The collision duration directly affects the calculation of average force exerted during the event. As collision time \( \Delta t \) decreases, a higher force is needed to bring the same change in momentum. In our example, \( \Delta t = 0.0055 \mathrm{~s}\), representing the short, intense moment the hand impacts the target.Knowing this duration is crucial for calculating and understanding the magnitude of forces involved. Even slight variations in collision time can lead to significant differences in the average force experienced, which has practical implications for the safety and performance of those practicing high-impact sports.