Velocity with negative acceleration

[PhysicsBoyMan]

Homework Statement

Train goes 20 m/s
Brakes cause a = -1 m/s²
Displacement at t = 40s ?

Homework Equations

v = 20 m/s
a = -1 m/s²
t = 40s

The Attempt at a Solution

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It seemed like this formula fit perfectly. It had all of the known variables and the one unknown neatly out front.

The velocity is too fast and the deceleration too slow for the displacement to be 0m.

The only thing I could think of was that my delta x should have data but the initial position is 0 and the final position is unknown.

I can't imagine where such a simple problem went wrong.

 

[AndrewHolowack]

If every second the train is going 1 m/s slower than it was the previous second how fast is it going after 20 seconds? Does that help?

 

[PhysicsBoyMan]

If every second the train is going 1 m/s slower than it was the previous second how fast is it going after 20 seconds? Does that help?

Is it really that simple though?

The first part of my equation is displacement = velocity x time without regard for acceleration. Before deceleration the train would go 800m.

I'm not sure how to represent your idea mathematically. Going -1 m/s² x 40s doesn't seem right to me.

 

[AndrewHolowack]

Your equation is right, and so is your answer if you assume that the negative acceleration continues for the entire 40 seconds. At 20 seconds the train comes to a stop and then begins to move backwards. At 40 seconds the train is back were you began with a velocity of -20 m/s. They way the question is worded you could argue that the train will simply come to a stop at 20 seconds.