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further velocity and acceleration (1 Viewer)

AFGHAN22

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a body moves in a straight line with initial velocity 9cm/s. its acceleration t sec after motion begins is 2(4-t) cm/s^2.
find how far the body moves before beginning to retrace its path, and prove that the elapsed time from the beginning of the motion before the particle returns to its starting point is 3(2+sq rt 7) sec.

answer : 162 cm (x= integral between ? (need to find) and 0 (8t -t^2+9) dt, to find time need to solve t^2 -12 t-27=0 by formula

please help guys especially and explanation of how the formula in the answer came about
 

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