Calculate the force to stop a train

[Apple&Orange]

Homework Statement

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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

Homework Equations

v = x / t

a = v / t

F = m a

The Attempt at a Solution

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v = x / t
33 = 150 / t
t = 4.55 secs

a = v / t
a = 33 / 4.55
a = 7.26 m/s^2

F = 3.6 * 10^5 * 7.26
F = 2613600N

Ignoring the sign convention for just a second, the answer is half the value of what I calculated. I would like to know why I have to use the formula below, and why my method is incorrect.

 

[TJGilb]

Your formula for acceleration is wrong. You were probably thinking of $a=\frac {dv} {dt}$. And your equation for velocity only works if the velocity is constant. In a case of changing velocity, like this one, the correct relationship is $v=\frac {dx} {dt}$. The solution is using the kinematic equation $v^2=v^2_0+2a\Delta x$ to solve for the required acceleration, and plugging it into your equation for force.

 

[TomHart]

As TJGilb pointed out, v = x/t is only valid for constant velocity - NOT constant acceleration. Therefore, your time calculation of t = 4.55 seconds is how long it would take the train to move 150 meters if it was traveling at a constant velocity of 33 m/s. Since the train is not moving at constant velocity, but decelerating, the time will take longer than 4.55 seconds to cover the 150 m distance. Because the time you calculated was shorter than the actual, your acceleration was greater than actual, which results in a greater required force than actual.

Just an observation: Superman probably could have moved the car with his little finger. Just sayin'.