An uncontrolled automobile traveling at 45 mph strikes a highway crash barrier square on. After initially hitting the barrier, the automobile decelerates at a rate proportional to the distance x the automobile has moved into the barrier; specifically, a=(-60)*sqrt(x) where a is experess as ft/s^2 and x as ft. Develope the plots for position vs time, velocity vs time and acceleration vs time for a vehicle initallity traveling at 40 mph, 50 mph and 60 mph.
So far I set the (-60)*sqrt(x) to v*(dv/dx) then rearranged the equation to get vdv=(-60)*sqrt(x). Then I integrated the dv side from Vinitial to Vfinal and the dx from 0 to Xfinal to find velocity in terms of position. Vfinal=sqrt(-80x^(3/2)+(Vi^2)).
I then set Vfinal equal to dx/dt so that sqrt(-80*xfinal^(3/2)+(Vinital^2))=dx/dt --> dt=dx/sqrt(-80x^(3/2)+(Vi^2)). Then I need to integrate the dt side from 0 to Tfinal and dx from 0 to Xfinal but doing that in matlab is where I get stuck. Then I have no clue how I can use matlab to rearrange the equation so that its position in terms of time and not time in terms of position.
