Question

(a) The position of a particle at time t is s(t) = t^3 + t. Compute the average velocity over the time interval [7, 12].(b) Estimate the instantaneous velocity at t = 7. (Round your answer to the nearest whole number)

Answer 1

Answer:

a) Average velocity = 278 units

b) Instantaneous velocity at t = 7 seconds is 148 units

Step-by-step explanation:

a) Average velocity is the ratio of displacement to time.

   We have

              s(t) = t³ + t

    t is in between 7 and 12

             s(7) =  7³ + 7 = 350

              s(12) = 12³ + 12 = 1740

    Displacement = 1740 - 350 = 1390

   Time = 12 - 7 = 5

  Displacement =  Average velocity x time

  1390 = Average velocity x 5

  Average velocity = 278 units

b) s(t) = t³ + t

   Differentiating

         v(t) = 3t² + 1

  At t = 7

          v(t) = 3 x 7² + 1 = 148 units

  Instantaneous velocity at t = 7 seconds is 148 units