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1. A particle is moving along a horizontal line with its position function given by 3(t) = t3 15t2 + 63: 51 Where s is in meters and t 2 0 is in seconds. Assume that the positive direction is to the right of the origin. (a) Determine the time interval(s) when the particle is moving to the left of the origin. (b) Where is the particle located at the second instance that it changed direction? ( ( c) Is the particle speeding up or slowing down at t = 6 seconds? d) Determine the total distance travelled by the particle during the rst 8 seconds