A particle of mass m moves in the x-y plane; its acceleration in m/s 2 is given

Question

A particle of mass m moves in the x-y plane; its acceleration in m/s2 is given by the expression a = 6i for t 0 secs. At t = 0 secs, the object is at the point (xo,yo) = (+36,0) where all coordinates are in meters. At t = 4 secs, the object is at the point (xo,yo) = (+36,+40).

(i) At what time (if any) in seconds is the particle at its maximum possible positive value of x? If there is no such maximum, state clearly why this is so.

(ii) At what time (if any) in seconds is the particle moving parallel to the x-axis?

(iii) Find the time t > 0 in seconds at which the particle crosses the y-axis.

Explanation / Answer

given datais particle mass m, acceleration a=-6i, initially at (xo,yo) = (+36,0),t = 4 secs, the object is at the point (xo,yo) = (+36,+40).

1)initally particle has max positive x value t=o,after that it does not get max positive value of x because it has negative acceleration

11)particle does not move parallel to the x axis at any time because its move perpendicular to the x axis

111)the particle cross the y axis that is it enters (-x,y) plane

xf=xi+at2   0=36-6*t2, t=root6=2.449sec

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