Position function of a particle is: s = t³ - 3t² - 5t ; t ≥ 0. When does particle reach velocity of 40 m/s?
This part of Calculus is called Applications. We should set up the problem, indicate the variables, write the formulas., ect. Can you help me do this step by step?
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3t^2 - 6t - 5 = 40
3t^2 - 6t - 45 = 0
3(t^2 - 2t - 15) = 0
3(t-5)(t+3) = 0
t = 5 or t = -3, but since t is greater than or equal to 0 we omit -3. Thus the particle reaches 40m/s at t = 5 sec.
take the derivitive of the function, which should come out to be 3t^2 -6t-5, set that equal to 40 and solve! Using a graphing calculator will make this a lot easier!