Calculating Time for an Airplane to Come to Rest Using Classical Mechanics

In summary, an airplane touching down at a speed of 100m/s and traveling 1000 metres along the runway with constant deceleration takes 20 seconds to come to rest. The equation used is Xf = Vi*t + 1/2 (Vf -Vi) * t. The formula for constant acceleration can also be used to find the acceleration first before finding the time using the simple form of energy conservation.
  • #1
Prototype44
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Homework Statement



An airplane touches down at a speed of 100m/s. It travels 1000 metres along the runway
while deceleration at a constant rate before coming to rest. How long did it take the airplane to come to rest on the runway?

Xi=0m/s Xf=1000m Vix=100m/s

Homework Equations


Xf=Xi+Vixt

The Attempt at a Solution


1000=0+100t
t=10s

Why is the answer 20 s? and why does this formula fail?
 
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  • #2
It seems that your particle isn't affected by any forces, thus it keeps on moving in the same direction with constant speed.
 
  • #3
the plane need decelation the speed from 100 m/s to 0 m/s so the mean velocity is 50 m/s then t = 20 s.
 
  • #4
Your math is correct, but your equation is wrong. I've calculated it and the answer
t=20s is correct. Try revisiting your equations.
 
  • #5
No, it's not wrong at all. you could use the equation and mean velocity. But if you need to use the standard equation. it will be
Xf = Vi*t + 1/2 a*t^2 (1)
Vf = Vi + a*t (2)
a = (Vf - Vi) /t (3)
Xf = Vi*t + 1/2 (Vf -Vi) * t
Xf = 1/2 (Vf +Vi)*t (4)
Xf = 1000 m , Vi = 100 m/s , Vf = 0 m/s
 
  • #6
Isn't this just constant acceleration motion? Just use the constant acceleration formulae to find the acceleration first.

Useful formulae:
v2 - vi2 = 2aΔx
v=vi + at
 
  • #7
yes, you are right.
You can use the simple form of energy conservation
1/2 m vf2 - 1/2 m vi2 = m a Δx
=> v2 - vi2 = 2aΔx
Thanks.
 

1. What is classical mechanics?

Classical mechanics is a branch of physics that studies the motion and behavior of macroscopic objects, such as planets, cars, and tennis balls. It is based on the laws of motion and gravity as described by Sir Isaac Newton in the 17th century.

2. What are the fundamental principles of classical mechanics?

The fundamental principles of classical mechanics are Newton's three laws of motion, which state that an object will remain at rest or in uniform motion unless acted upon by an external force, the force acting on an object is equal to its mass times its acceleration, and for every action, there is an equal and opposite reaction.

3. What is the difference between classical mechanics and quantum mechanics?

Classical mechanics deals with the behavior of macroscopic objects, while quantum mechanics deals with the behavior of microscopic objects, such as atoms and subatomic particles. Additionally, classical mechanics follows deterministic laws, while quantum mechanics follows probabilistic laws.

4. What are some real-world applications of classical mechanics?

Classical mechanics has many real-world applications, including understanding the motion of planets and satellites, designing and analyzing machines and structures, predicting the trajectories of projectiles, and calculating the forces and stresses on buildings and bridges.

5. How has classical mechanics evolved over time?

Classical mechanics has evolved significantly over time, with contributions from scientists such as Galileo, Newton, and Einstein. It has been refined and expanded upon to explain more complex systems and phenomena, such as relativity and quantum mechanics. Additionally, advancements in technology have allowed for more precise measurements and calculations within classical mechanics.

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