A particle moves along the x-axis in such a way that its position at time t is given by x=2t3-15t2+24t+3, where x is in metres and t is in seconds. (i) Determine the velocity and acceleration of the particle at time t. (ii) At what values of t is the particle at rest? (iii) What is the velocity when the acceleration is first zero? (iv) Calculate the distance travelled by the particle in the first 3 seconds.
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