In this lab we were asked to anylaze footage of a Mini's test crash. We viewed the crash in terms of the dummy's velocity, position, and acceleration at different points in the crash.
In the graph above, both velocity (triangles) and position (circles) are plotted against time.
To get the velocity before the crash we looked only at data recorded beforehand (we went up to about 4.5 seconds). We took the derivative, or slope, of our position vs. time graph, which shows our velocity before the crash to be -1.043 m/s. We then checked this to the velocity vs. time graph. The two answers were very close, in the velocity vs. time graph our mean speed was -1.052m/s.
We found the acceleration before the crash by taking the derivative/slope of the velocity vs. time graph. This gave us an acceleration of 1.188 m/s/s. During the lab, Mr. Hampshire asked our group why the coefficient A in the equation for our position vs. time graph was almost exactly half of our acceleration. This fits in with the position equation: x = 1/2at^2. The coeffecient A is half the acceleration because the position equation requires us to halve the acceleration.
The position of the passenger is given by the quadratic equation of the curved best fit line of our position vs. time graph: x = At^2 + Bt + C. Once we plug in the values of our coefficients and constant we get the equarion x = .6040t^2 -6.905t + 21.8 to represent the dummy's position.
The last aspect of this lab poses the question: Would we like to own a Mini? I, personally, would not. The are small, low to the ground, and even though the recieve good crash test ratings, I find it hard to believe that such a tiny car could stand up to the huge SUVs common in Dallas.
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