Question

Relation between distance covered and time of
moving particle is s = 2t³ - 4t² + 3t. What will be the
velocity and acceleration after 3sec?​

Answer 1

Answer :

Relation between distance covered and time of moving particle is provided$.$

• s = 2t³ - 4t² + 3t

We have to find velocity and acceleration of particle after 3s.

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◈ Instantaneous velocity :

➳ v = (Δt ➝ 0) Δs/Δt = ds/dt

➳ v = d(2t³ - 4t² + 3t)/dt

➳ v = 6t² - 8t + 3

➳ v = 6(3)² - 8(3) + 3

➳ v = 6(9) - 24 + 3

➳ v = 54 - 21

➳ v = 33 m/s

◈ Instantaneous acceleration :

⇒ a = (Δv ➝ 0) Δv/Δt = dv/dt

⇒ a = d(6t² - 8t + 3)/dt

⇒ a = 12t - 8

⇒ a = 12(3) - 8

⇒ a = 36 - 8

⇒ a = 28 m/s²