Question

the displacement of a particle is given by X=7t³-5t². Find its initial velocity for the interval 2 to 5 second , acceleration at t=1sec.​

Answer 1

  Answer:

        V₁ = 64ms⁻¹

        V₂ = 475ms⁻¹

         a = 32ms⁻²

Explanation:

In this question we must use derivatives

X=7t³-5t²                                                    [d axⁿ / dx = a  dxⁿ /dx = a nxⁿ⁻¹]

V = dx / dt

V = d 7t³-5t² / dt

V = 7 × 3t³⁻¹ - 5 × 2t²⁻¹

V = 21t² - 10t

when t = 2s  ,    V₁ = 21 × 2² - 10 × 2

                           V₁ = 21 × 4 - 20

                           V₁ = 84 - 20

                      V₁ = 64ms⁻¹

when t = 5s        V₂ = 21 × 5² - 10 × 5

                           V₂ = 21 × 25 - 50

                           V₂ = 525 - 50

                    V₂ = 475ms⁻¹

acceleration (a)

a = dv / dt

a = d 21t² - 10t / dt

a = 21 × 2t - 10

a = 42t - 10

at t = 1s  ,  a = 42 × 1 - 10

                a = 42 - 10

             a = 32ms⁻²

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