The angle∅ swept by a particle moving round a circle at time t is given by ∅=t^3+3t-5. Find the angular velocity and acceleration at t=5s

Answer 1

To find the angular velocity and acceleration at t = 5s, we need to find the first and second derivative of the angle with respect to time (∅ = t^3 + 3t - 5).

First derivative:
∅' = 3t^2 + 3

Second derivative:
∅" = 6t

Now, we can substitute t = 5s into the derivatives to find the angular velocity and acceleration at t = 5s.

Angular velocity at t = 5s:
∅'(5) = 3(5)^2 + 3 = 3(25) + 3 = 75 + 3 = 78 rad/s

Therefore, the angular velocity at t = 5s is 78 rad/s.

Angular acceleration at t = 5s:
∅"(5) = 6(5) = 30 rad/s^2

Therefore, the angular acceleration at t = 5s is 30 rad/s^2.