Need to compute distance during during acceleration of a train

vendredi 30 août 2013

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

A train is traveling down a straight track at 20 m/s when the engineer applies the brakes, resulting in an acceleration of -1.0 m/s² as long as the train is in motion. How far does the train move in a 40-s time interval starting at the instant the brakes are applied?

2. Relevant equations

[itex]\Delta[/itex]x = v₀t + (1/2)at²

3. The attempt at a solution

Answer from the back of the book: 200 m, but my answer does not agree!

[itex]\Delta[/itex]x = v₀t + (1/2)at²

[itex]\Delta[/itex]x = (20 m/s)(40 s) + (1/2)(-1.0 m/s²)(40 s)²

[itex]\Delta[/itex]x = 800 m + (1/2)(-1,600 m)

[itex]\Delta[/itex]x = 800 m - 800 m

[itex]\Delta[/itex]x = 0 m

This has to be wrong! I have gone over the calculations and the equation numerous times, and I can't find anything wrong though. Can anyone help?

Thanks!