91Ó°ÊÓ

Velocity is a key concept in physics, especially when discussing motion. It describes the rate at which an object changes its position. Unlike speed, which is a scalar quantity that only tells us how fast something is moving, velocity is a vector. This means it includes both the speed and the direction of the object's motion.
In our problem, the airplane's initial velocity is given as 300 mph. This is essentially the speed at which the airplane is moving at that specific moment in time. As the airplane accelerates, its velocity changes, affecting both how fast it is going and impacting its overall path.

Acceleration measures how quickly velocity changes over time. It is often expressed in units like meters per second squared or miles per hour per hour (as in this problem).
In the airplane exercise, its acceleration is 200 mph per hour. This means every hour, its velocity increases by 200 mph if the acceleration remains constant. Acceleration is critical when calculating changes in velocity over time, determining how quickly things speed up or slow down.

Sometimes, time needs to be converted from one unit to another to simplify calculations, especially when dealing with acceleration. When time is given in minutes, but acceleration is measured in hours, converting minutes to hours is necessary to maintain consistent units.
In the given exercise, we need to convert 5 minutes into hours. Since there are 60 minutes in an hour, 5 minutes corresponds to \( \frac{5}{60} \) hours, or equivalently, \( \frac{1}{12} \) hours. This conversion allows us to accurately calculate the change in velocity using the acceleration provided.

The constant acceleration formula is vital for calculating how an object's speed changes over a set duration, provided the acceleration is steady. This principle is commonly expressed as \( \Delta v = a \cdot t \), where \( \Delta v \) is the change in velocity, \( a \) is acceleration, and \( t \) is the time period over which the acceleration applies.
For the airplane, the change in velocity is calculated by multiplying the given acceleration (200 mph per hour) by the converted time (\( \frac{1}{12} \) hours). The resulting 16.67 mph represents how much the airplane's speed will increase after 5 minutes. Adding this change to the initial speed (300 mph), we find the aircraft will travel at 316.67 mph after the 5-minute interval.