Question

The position of the particle is given by x=6t2-2t+3. Find (a) Its initial position (b) instantaneous velocity at 3s (c) instantaneous acceleration at t=2s (d) average velocity between t=2s and t=3s

Answer 1

Answer:

Explanation:

(a) x = (6t²-2t + 3)m

finding initial position means to find position at t = 0

therefore , initial position = 6(0)² - 2(0) + 3

                                            = 3 m

(b) v = dx/dt

=> v = d(6t² - 2t + 3)/dt

=> v = (12t - 2) m/s

after 3 sec ,

v(instantaneous) = 12(3) - 2

                              = 36 - 2 = 34 m/s

(c) a = dv/dt

       = d(12t - 2)/dt

       = 12 m/s²

    particle has constant acceleration ,

    so after 2 sec. acceleration = 12m/s²

(d) average velocity = Δx/Δt

                                 = (6(3)² - 2(3) + 3) - (6(2)² - 2(2) + 3)/3-2

                                  = 28 m/s

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