# 1D-kinematics with constant acceleration

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1. Feb 15, 2015

### 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/ [Broken]

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

2. Relevant equations
a=dv(t)/dt
x(t)=x0 +∫v(t)dx

3. 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

Last edited by a moderator: May 7, 2017
2. Feb 15, 2015

### azizlwl

Just add the area under the line.

3. Feb 15, 2015

### 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?

4. Feb 15, 2015

### Elvis 123456789

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

5. Feb 15, 2015

### TSny

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

6. Feb 15, 2015

### 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?

7. Feb 15, 2015

### TSny

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

8. Feb 15, 2015

### Elvis 123456789

Yes you are right, thank you friend!