91Ó°ÊÓ

Equations of motion are mathematical formulas used in physics to describe the motion of an object. They connect different physical quantities like velocity, acceleration, displacement, and time. These equations help us find missing information when certain parameters are known.
In the exercise provided, we utilized two main equations of motion:

• First equation:
  \( v = u + at \)
  Here, \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time taken. This equation helps us find out the change in velocity over time due to acceleration.
• Second equation:
  \( s = ut + \frac{1}{2}at^2 \)
  In this formula, \( s \) is the displacement, which shows the distance covered by the object. The term \( ut \) represents the distance covered by the object moving at initial velocity \( u \) for time \( t \), while \( \frac{1}{2} a t^2 \) accounts for the additional displacement due to acceleration over time.

\ With these equations, one can trace the path of an object under uniform acceleration, making predictions and answering practical questions such as how long a jet needs to stop or if a runway is long enough.

Acceleration is a measure of how quickly the velocity of an object changes. It is a vector quantity, meaning it has both magnitude and direction.
In practical scenarios like the problem given, acceleration is a crucial factor. The jet plane's deceleration, which is negative acceleration, tells us how swiftly it can reduce its speed.
### Types of Acceleration

• Positive Acceleration: When an object speeds up, its acceleration is positive.
• Negative Acceleration (Deceleration): When an object slows down, as with the jet, its acceleration is negative.

Important points to remember:
- Acceleration is measured in meters per second squared \( \mathrm{m/s^2} \).
- Deceleration here is \(-5 \mathrm{~m/s^2}\), showing how quickly the plane decreases its velocity until stopping.
By analyzing acceleration, we can determine precisely how much time it takes for an object to come to rest or to achieve a certain velocity when moving in a straight path.

Displacement refers to the change in position of an object. It is also a vector quantity and differs from distance because it considers direction.
In the problem, we were required to calculate how far the plane travels before coming to a stop.
### Key Features of Displacement

• Displacement takes direction into account, unlike distance, which measures only the path length an object travels.
• If an object returns to its starting position, its displacement is zero, even if it covered a considerable distance.

To solve for displacement, we used the equation:
\( s = ut + \frac{1}{2}at^2 \). This provides us with the total path covered taking into account initial speed, acceleration, and time.
- **Result:**
The jet covers \(1000 \mathrm{~m}\) (or \(1 \mathrm{~km}\)) before it stops, exceeding the \(0.800 \mathrm{~km}\) runway limit. Thus, understanding displacement is essential for making practical decisions about whether the plane can safely land within a given space.