A particle moves in a straight line so that the displacement, s metres, from a fixed-point O,

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A particle moves in a straight line so that the displacement, s metres, from a fixed-point O, is given by s = 2t3 – 17t2 + 40t - 2, where t is the time is seconds after passing a point X on the line.

a. Find the distance OX.

b. Find the value of t when particle is first at rest.

c. Find the values of t for which the velocity is positive.

d. Find the values of t for which the velocity is negative.

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