1. Create an equation for the velocity of a particle at any time t, stating the...

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1. Create an equation for the velocity of a particle at any time t, stating the initial position, which cannot equal 0. The equation must include the following: Rational function; f(t) = P(t) Q(t) Trigonometric function - the trigonometric function must be part of the rational function a. Determine the displacement of the particle in the first 10 seconds using a suitable numerical method. i. Explain how this estimation could be made more exact. b. Determine the exact displacement of the particle for the first 10 seconds, and then determine the exact location of the particle after 10 seconds. c. Determine the expression for acceleration of the particle. Determine the average acceleration of the object between 0 and 10 seconds using the average ordinate expression; Yavg = b-a a f(x)dx as outlined in your textbook in section 34-3. 1. Create an equation for the velocity of a particle at any time t, stating the initial position, which cannot equal 0. The equation must include the following: Rational function; f(t) = P(t) Q(t) Trigonometric function - the trigonometric function must be part of the rational function a. Determine the displacement of the particle in the first 10 seconds using a suitable numerical method. i. Explain how this estimation could be made more exact. b. Determine the exact displacement of the particle for the first 10 seconds, and then determine the exact location of the particle after 10 seconds. c. Determine the expression for acceleration of the particle. Determine the average acceleration of the object between 0 and 10 seconds using the average ordinate expression; Yavg = b-a a f(x)dx as outlined in your textbook in section 34-3.