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

[Prototype44]

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?

 

[dikmikkel]

It seems that your particle isn't affected by any forces, thus it keeps on moving in the same direction with constant speed.

 

[Twich]

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.

 

[Saxby]

Your math is correct, but your equation is wrong. I've calculated it and the answer
t=20s is correct. Try revisiting your equations.

 

[Twich]

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

 

[HSSN19]

Isn't this just constant acceleration motion? Just use the constant acceleration formulae to find the acceleration first.

Useful formulae:
v² - v_i² = 2aΔx
v=v_i + at

 

[Twich]

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.