1D-kinematics with constant acceleration

[Elvis 123456789]

1. A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time the figure..... http://postimg.org/image/4q40kyrnx/

What distance does the cat move from t=0 to t=7.5s?

Homework Equations

a=dv(t)/dt
x(t)=x0 +∫v(t)dx

The Attempt at a Solution

From the graph I got v(t)=(-4/3)*t + 8

I integrated and got x(t)=(-4/6)*t^2 + 8*t
I evaluated at the the upper and lower limits and got 22.5 cm for the answer but got it wrong[/B]

 

[azizlwl]

Just add the area under the line.

 

[TSny]

Hello, and welcome to PF!

Your work looks good for finding x(t). You are asked for the distance traveled. Is that the same thing as the displacement?

 

[Elvis 123456789]

I thought that was how you're supposed to solve for distance traveled. I don't really know what else to do.

 

[TSny]

Does the cat ever turn around and walk back in the opposite direction? Did you take that into account?

 

[Elvis 123456789]

So then at -4/3*t + 8=0 the cat reaches its maximum displacement of 24 cm @ t=6s. and at t=7.5s the cat is at 22.5 cm, so the distance is equal to 24cm + 1.5cm= 25.5cm?

 

[TSny]

Yes, at least that's what I would interpret as distance traveled.

 

[Elvis 123456789]

Yes you are right, thank you friend!