(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The figure below represents part of the performance data of a car owned by a proud physics student. (The horizontal axis is marked in increments of 1 s and the vertical axis is marked in increments of 1 m/s.)

Here's a picture:

http://i.imgur.com/6bGXd.png

(d) Write an equation for x as a function of time for each phase of the motion, represented by the segments 0a, ab, and bc. (Use the following variable as necessary: t.)

2. Relevant equations

I know that I have to integrate the various line segments since the integration of velocity is displacement

3. The attempt at a solution

Now, treating the graph as a group of straight lines, in line segment 0a, I approximated the coordinates as (0,0) and (7.5,25) and got the slope, 3.33, since it's a line, the v(t) is 3.33t. Then, integrated in terms of t, and got (1/2)3.33t^2. That one was correct.

The problem comes when I try to get the displacement functions for ab and bc. Now, in line segment ab, I got that the function, since it's a straight line, v(t) is just 25. So, I thought the displacement function would just be 25t. But, apparently, I'm way off, since they got 25t+-93.75. Which...is confusing. I have no idea where they got that.

And in bc, I don't even have a clue what they did.

I think I'm missing something here. Anyone mind helping me out?

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# Kinematics Physics (Relating velocity/time graph to displacement/time)

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