For 4.95 seconds, a particle moves in a straight line according to the position functionf(t) = (t³ + 1)(5 – t) – 5where t is measured in seconds and f in feet.You can visualise this motion and verify many of your answers using a graph. First attemptall the problems by hand, and then graph the position function to verify your answers.a) What is the position of the particle at t = 0, t = 1, t = 2, t = 4.95?b) Find the velocity of the particle at time t. What is the velocity of the particle at t = 0,t = 1, t = 2, t = 4.95?c) When is the particle at rest? When is the particle moving forward? d) Find the total distance traveled by the particle on the intervals [0, 1] and [1,2]. Whichis larger and why?e) Find the acceleration of the particle at time t.f) When was the particle speeding up? Slowing down?

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Answered: Ime f(t) = (t3 + 1)(5 – t) – 5 where t…

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