# Application of one dimensional force - Dynamics

1. Nov 11, 2014

### Paul W.

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

Superman must stop a 120-km/hr train in 150 m to keep it from hitting a stalled car on the tracks. If the trains mass is 3.6 x 10^5 kg, how much force must he exert?

Vi = 33 m/s (120 km/h)
Vf = 0 m/s
Displacement (Xf - Xi) = 150 m
M = 3.6 x 10^5 kg

2. Relevant equations

Vf^2 = Vi^2 + a(Xf - Xi) - used to calculate the acceleration without a time value.

F = Ma - used to calculate the force required to stop the train with the calculated acceleration.

3. The attempt at a solution

First convert Km/h to m/s. (120*1000)/60^2 ~ 33 m/s

Then find the acceleration.
A = (Vf^2 - Vi^2)/(Xf - Xi)
A = -(33 m/s)^2 / 150 m ~ -7.3 m/s^s

Now calculate the force required to achieve that acceleration.

F = Ma
F = 3.6 x 10^5 kg* -7.3 m/s^2
F ~ -2.6 x 10^6 N

The answer at the back of the book is half that value. (1.3 x 10^6 N) I don't understand what I'm doing wrong.

2. Nov 11, 2014

### PhanthomJay

Oh your work is good but you forgot the 2!

Vf^2 = Vi^2 + 2a(Xf - Xi)

3. Nov 11, 2014

Oh FFS.

Thank you.