Interpreting and converting an acceleration-time graph

[ACSC]

Homework Statement

Homework Equations

a = Δv/Δt
v = Δx/Δt
x = area under velocity graph

The Attempt at a Solution

According to my second attempt, the answer to "particle's speed at t = 20.0 s?" is not 15m/s either.
Working out picture.
I don't understand where I went wrong. I've always thought that the area under a velocity graph would give the distance.
If t=20s isn't v=15m/s, then maybe that's why? But according to the a-t graph, 5x-3=-15. :S

 

[Ibix]

Take another look at your graph for the deceleration phase. It slows down by 15m/s.

 

[ACSC]

Take another look at your graph for the deceleration phase. It slows down by 15m/s.

Oh... I see now. It doesn't slow down to 15m/s but slows down 15m/s.
So like this, right?

 

[SammyS]

Oh... I see now. It doesn't slow down to 15m/s but slows down 15m/s.
So like this, right?
[ IMG]http://i.imgur.com/lL42HNY.png[/PLAIN]

That looks good !

 

[Nickie]

As a scientist, it is important to always double check your work and make sure your calculations are correct. In this case, it seems like there may be an error in your calculation for the particle's speed at t=20s.

To interpret and convert an acceleration-time graph, it is important to remember the equations a=Δv/Δt and v=Δx/Δt. The area under the velocity graph does indeed give the distance, but in this case, we are looking for the particle's speed at a specific time, not the distance it has traveled.

To find the particle's speed at t=20s, we can use the equation v=Δx/Δt. From the given a-t graph, we can see that the acceleration is constant at -3 m/s^2. This means that the velocity is decreasing by 3 m/s every second.

At t=20s, the particle's initial velocity was 15 m/s (from t=0s to t=10s, the velocity was constant at 15 m/s). So, at t=20s, the particle's velocity would have decreased by 3 m/s for 10 seconds, giving a final velocity of 15-3(10) = -15 m/s.

Therefore, the correct answer to "particle's speed at t=20.0s?" is -15 m/s. It is important to always double check your calculations and make sure they align with the given information and equations.