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Ime f(t) = (t3 + 1)(5 – t) – 5 where t is measured in seconds and f in feet. You can visualise this motion and verify many of your answers using a graph. First attempt all 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 att = 0, t = 1, t = 2, t = 4.95? c) When is the particle at rest? When is the particle moving forward?

Ime f(t) = (t3 + 1)(5 – t) – 5 where t is measured in seconds and f in feet. You can visualise this motion and verify many of your answers using a graph. First attempt all 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 att = 0, t = 1, t = 2, t = 4.95? c) When is the particle at rest? When is the particle moving forward?

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For 4.95 seconds, a particle moves in a straight line according to the position function f(t) = (t³ + 1)(5 – t) – 5 where t is measured in seconds and f in feet. You can visualise this motion and verify many of your answers using a graph. First attempt all 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?
Transcribed Image Text:For 4.95 seconds, a particle moves in a straight line according to the position function f(t) = (t³ + 1)(5 – t) – 5 where t is measured in seconds and f in feet. You can visualise this motion and verify many of your answers using a graph. First attempt all 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]. Which is larger and why? e) Find the acceleration of the particle at time t. f) When was the particle speeding up? Slowing down?
Transcribed Image Text:d) Find the total distance traveled by the particle on the intervals [0, 1] and [1,2]. Which is 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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