A plot of acceleration versus time for a particle is shown

[suspenc3]

Homework Statement

A plot of acceleration versus time for a particle is shown. Whats the difference between its position at t=4s and t=0s if v(0)=-4m/s.

http://img441.imageshack.us/img441/532/dynmc8.th.png

Homework Equations

The Attempt at a Solution

Ive been working on this problem for hours until I thought I solved it...I got the right answer but I realized after that I made a mistake..but still got the right answer. After I tried to do it the right way i keep getting the wrong answer.

v(0)=-4m/s
v(1)=16m/s (since constant acceleration from 1s to 2s)

$$a_{12} = -20t+40 = dv/dt$$ - y=mx+b, for the non-uniform section (1s-2s)

now I rearrange the above and integrated to find v(2)

$$\int_{v(1)}^{v(2)}dv = \int_1^2 -20t+40dt$$

This is where I made my mistake, instead of using v(1) I used v(0)=-4m/s

continuing...$$v(2)-(-4m/s)=-10t^2+40t |_1^2$$

solving gives v(2)=26m/s

Now I integrated again...$$-10t^2+40t = dx/dt$$ to find the displacement for the non-uniform section...giving me an answer of 68/3.

Anyways..add all the displacements up and I end up with 80.66 which is the right answer. How come when I try and use v(1)=16m/s for my lower limit in the first integration I keep getting wrong numbers?

Any help would be appreciated

 

[Astronuc]

It is difficult to read the variable on the vertical axis of the plot, which looks like x, or position, rather than acceleration.

If the plot is acceleration, and the vertical axis is at t=0, then the acceleration is constant 20 m/s² through t = 1s, then it decreases linearly between 1 and 2 to zero, after which there is no acceleration from t = 2s to 4s (so for the last two seconds, it's coasting at constant velocity).

 

[piercas]

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it is important to carefully analyze and interpret data to ensure accuracy in our conclusions. In this case, it seems that there may have been a mistake made in the initial approach to solving the problem. However, it is commendable that you were able to recognize this mistake and still arrive at the correct answer. It is important to double-check and verify our calculations to ensure accuracy and avoid potential errors. It may be helpful to review the steps and equations used in solving the problem to identify where the mistake was made. Overall, it is important to approach problems with a critical and analytical mindset, and to continually strive for accuracy and precision in our scientific work.