To find the angular velocity and acceleration at t=5s, we need to find the derivative of the given function.
Given ∅ = t^2 + 3t - 5, we can find the angular velocity by taking the derivative with respect to t:
ω = d∅/dt = d/dt (t^2 + 3t - 5)
To find the acceleration, we take the second derivative of ∅ with respect to t:
α = d²∅/dt² = d/dt (d∅/dt) = d/dt (t^2 + 3t - 5)
First, let's find the angular velocity:
ω = d∅/dt = 2t + 3
Now, let's find the acceleration:
α = d²∅/dt² = d/dt (2t + 3) = 2
Therefore, the angular velocity at t=5s is:
ω = 2(5) + 3 = 13 rad/s
And the angular acceleration at t=5s is:
α = 2 rad/s²
The angle∅ swept by a particle moving round a circle at time t is given by ∅=t^2+3t-5. Find the angular velocity and acceleration at t=5s
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