Question

The angle turned through by the fly wheel in a time interval t Is given by θ = at + bt^2 + ct^3 where a,b,c are constant where a,b,c are constant. The angular velocity a t = 2s is

Answer 1

Given :-

• The angle turned through by the fly wheel in a time interval t Is given by θ = at + bt² + ct³ where a,b,c are constant where a,b,c are constant. The angular velocity a t = 2s is

Solution :-

• Here, angular displacement is given to us. We need to find angular velocity at t = 2s.
• We know that, angular velocity and angular displacement are related as :-

      ω = $\sf\frac{d\theta }{dt}$

       Where :-

      → ω is angular velocity

      → θ is angular displacement

• In the question, it is given that, θ = at + bt² + ct³. So,

         ω = $\sf\frac{d}{dt}(at + bt^{2} + ct^{3})$

     ⇒ ω = a + 2bt + 3ct²    ------------------- (1)

• As they asked angular velocity at t = 2s, let us substitute t = 2s in equation (1)

     ⇒ ω = a + 2b(2) + 3c(2)²

     ⇒ ω = a + 4b + 12c

∴ The angular velocity of the fly wheel at t = 2s is a + 4b + 12c

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Answer 2

Answer is a + 4b + 12c