MASTERY QUESTION
A train moving at vo = 15 m/s passes the origin (xo = 0) at to = 0.  At that instant, the engineer hits the brakes, giving the train an acceleration of - 0.5 m/s2, so that it comes to a stop.  Where is the train after 40 seconds?

Let's try the problem two ways using different kinematic equations:

1)
x = xo + vot + 1/2at2
x = 0 + 15*40 + 1/2(-0.5)*(402) = 200 m

2)
v2 = vo2 + 2a(x - xo)
Set vf = 0 ( the train comes to rest) and solve for x:
x = [v2 - vo2 ]/2a + xo = [02 - 152]/2(-.5) + 0 = 225 m

Two different answers using two approaches; that can't be good.  Which is correct?  It turns out that the train actualy comes to rest after 30 seconds:
v = vo + at
Set vf = 0 and solve for t:
t = [v - vo]/a = [0 - 15]/(-0.5) = 30 s.
Equation 1 assumes that the acceleration of the train was the same throughout the full 40 seconds, i.e., that the train stopped and then began to move backward, in this case 25 m in 10 seconds.

Was this a trick question?  No.  It serves to remind us not to use equations blindly.  Not all of the information in the problem is reflected in the equations.  Remember that one assumption we used when we derived the kinematic equations was that the acceleration is constant.  That is not the case in this problem.

Should we have known in advance which relationship would give us the correct answer?  No.  Indeed, if the numbers had been slightly different, then the first equation might have been the appropriate one, with the train not yet at rest at the end of 40 seconds.