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

Consider the plot below describing the acceleration of a particle along a straight line with an initial position of −15 m and an initial velocity of −3 m/s.

A) What is the velocity at 5 s? Answer in units of m/s.

B) What is the position at 5 s? Answer in units of m.

2. Relevant equations

v = v_{0}+ (a)(t)

3. The attempt at a solution

A) Because the acceleration is obviously not constant, I added the periods of constant acceleration, from 0 to 2 seconds and 2 to 5 seconds as so:

v= -3 + (7)(2) = 11

v= 11 + (1)(5) = 16

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27 (answer)

I'm pretty sure that I'm wrong, and I'm confused about a couple of things:

1. Is the initial velocity always going to be -3 m/s, or is it going to be the velocity that was the end point of the other equation? Because above, I got 11 m/s for the first equation - does that mean that 11 m/s will be my initial velocity for the second equation (when I'm doing the second part of the graph) as well? Or will it be -3 m/s?

2. I know this is a stupid question, but is the time variable a change in time, in other words, the final time minus the time you're starting at? Like looking at the graph, from the interval from 2 to 5 seconds when the acceleration is constant, is "t" 3 seconds, the change in time, or is it 5 seconds, the final time the acceleration is constant? I'm confused as to what to use.

Once I get that squared away, I'll be able to focus on part "B" of the problem.

Thanks for the help!

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# Using a graph to find velocity and position at a said time

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