Calculating the Initial Velocity of an Airliner Using Kinematic Equations

Understanding the motion of an object is crucial in various fields, including aviation. In this article, we explore how to determine the initial velocity of an airliner using the kinematic equation. We provide a detailed step-by-step solution to calculate the initial velocity of an airliner that experiences a constant acceleration during takeoff.

Introduction to Kinematic Equations

Kinematic equations are fundamental in physics, used to describe the motion of objects without considering the forces acting on them. There are four key equations:

( s ut frac{1}{2}at^2 ) ( v u at ) ( v^2 u^2 2as ) ( s frac{1}{2}(u v)t )

For this problem, we will use the equation ( v u at ) which is derived from the second equation. This equation allows us to calculate the initial velocity ( u ) given the final velocity ( v ), acceleration ( a ), and time ( t ).

Problem Statement

An airliner experiences an average acceleration of ( 8.4 , m/s^2 ). If the plane accelerates for 4.2 seconds and has a final velocity of ( 41.1 , m/s ), what was the initial velocity of the plane?

Step-by-Step Solution

The given values are:

( v 41.1 , m/s ) ( a 8.4 , m/s^2 ) ( t 4.2 , s )

We need to find the initial velocity ( u ). The kinematic equation to use is:

( v u at )

Substitute the given values into the equation:

( 41.1 u 8.4 times 4.2 )

Calculate the product ( 8.4 times 4.2 ):

( 8.4 times 4.2 35.28 )

So the equation becomes:

( 41.1 u 35.28 )

Isolating ( u ) by subtracting 35.28 from both sides:

( u 41.1 - 35.28 )

Therefore, the initial velocity ( u ) is:

( u 5.82 , m/s )

Conclusion

By using the kinematic equation ( v u at ), we calculated that the initial velocity of the airliner is ( 5.82 , m/s ). This demonstrates the practical application of kinematic equations in aviation, where precise calculations are essential for safe and efficient takeoffs and landings.

Relevant Keywords

initial velocity, kinematic equation, airliner acceleration