# Classical Mechanics Questions

1. Apr 14, 2012

### Prototype44

1. The problem statement, all variables and given/known data

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

2. Relevant equations
Xf=Xi+Vixt

3. The attempt at a solution
1000=0+100t
t=10s

Why is the answer 20 s? and why does this formula fail?

Last edited: Apr 15, 2012
2. Apr 14, 2012

### dikmikkel

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

3. Apr 14, 2012

### 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.

4. Apr 14, 2012

### Saxby

t=20s is correct. Try revisiting your equations.

5. Apr 15, 2012

### 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

6. Apr 15, 2012

### HSSN19

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. Apr 17, 2012

### 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.