Finding Velocity from Acceleration Graph

[Nitrate]

Homework Statement

Find each particle's velocity at t=7.0s. Work with the geometry of the graphs, not with kinematic equations.

Homework Equations

The Attempt at a Solution

I'm not sure how to arrive at an answer. For the previous question (velocity from graph b) I found the value of -20 m/s by reading the graph and before that (velocity from graph a) I did a simple delta/delta[t] calculation and got -10 m/s. My issue is that I can't find an velocity at t=7.0s for graph C (the acceleration graph.) Please help.
Thank you.

 

[Ibix]

Velocity is the integral of acceleration with respect to time. How could you read that off a graph?

 

[Nitrate]

Velocity is the integral of acceleration with respect to time. How could you read that off a graph?

by integrating the area at that point to the x axis?
1/2(2)(-20)
?

 

[Ibix]

Integration is right, presuming you meant to the y axis. I don't think you've got to the right answer though, since there's more than one triangle to worry about in the 0-7s region of the graph. You can check your answer by counting squares for a graph this simple.

Remember that the integral just gives you the velocity change over the time period, which isn't quite what you're asked for.

 

[Nitrate]

Integration is right, presuming you meant to the y axis. I don't think you've got to the right answer though, since there's more than one triangle to worry about in the 0-7s region of the graph. You can check your answer by counting squares for a graph this simple.

Remember that the integral just gives you the velocity change over the time period, which isn't quite what you're asked for.

how would i isolate

 

[azizlwl]

Find a(t) and do antiderivative to find v(t).

 

[Nitrate]

still can't get it.
i tried calculating the area underneath both of those and got 10 m/s, but that wasn't the velocity of the acceleration graph... I am not sure what to do

 

[Nitrate]

as much as i hate to ask for a straight answer (with a minor explanation) from you guys, i think it would be beneficial because i simply can't get it and I've inputted about 12 answers into this program

 

[Ibix]

Complete answers are forbidden by forum rules.

The area under the graph can be obtained by counting squares between the graph and the x-axis, remembering that the area is negative when the graph is below the axis. Each square is 1s wide and 10ms^-2 high. To start you off, the area between 5s and 7s is -20ms^-1. You can work out the area between 0s and 5s.

Do remember that the result is the velocity gain over the period, not the final velocity.