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

Answer 1

To find the acceleration at t = 5s, we need to take the second derivative of the angle function ∅(t).

First, find the first derivative of ∅(t) with respect to t:
∅'(t) = d(∅)/dt = d(t^3+3t-5)/dt = 3t^2+3

Next, take the second derivative of ∅(t):
∅''(t) = d(∅'(t))/dt = d(3t^2+3)/dt = 6t

Now, substitute t = 5s into ∅''(t) to find the acceleration at t = 5s:
∅''(5) = 6(5) = 30

Therefore, the acceleration at t = 5s is 30.