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

Answer 1

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