Find Velocity when Acceleration Vs Time Graph

[dgales4130]

Homework Statement

Find the particles Velocity at 7 seconds . ( Graph Below)

Homework Equations

The Attempt at a Solution

T=5 from 7-2
or
T=2 From 7-5 ( Because It's now -a)

I tried int from 0 to 5 -10dt and got -50
then AT=v with both
A @ 7 second = (-20*2)/2 = -20

Is velocity not negative.
I am really embarrassed to ask for help. I would love to understand , and maybe remind me some how science is fun ..

 

[daveb]

I will assume you are familiar with differentiation since it's listed under relavant equations. Do you know integration yet? If not, think about the graph of a constant acceleration - how do you find the velocity of a constant acceleration versus time graph?

 

[dgales4130]

Yes , I am comfortable with doing integration.

In this case I am not sure what is area. I know that area is from t 0 - 5 is on the positive side . I am not sure if I should add the two areas to find the v at 7s or something else.

I haven't had I chance to talk about negative area to so it's just a bunch of assumitions , which I don't like.

So , Should I find the area of the partial triangle then the other one below axis ?

Or something else ?

 

[dgales4130]

If I just do are both on the positive side and negative side of the a axis i get the quantities

20 ( t , 1-2 ; up tri )
20 (t 1-2 ; below rectangle )
45 (t 2-5 ; large tri )
20 ( t 5-7 ; tri in 4 quadrant ) ( is this positive or negative area )