
Enrique S. answered 11/08/20
AP Calculus AB Teachers for 7+ years
Hi Anayza,
Particle motion problems are probably some of the funnest stuff to work on for AP Calculus.
First thing to know is that acceleration is the derivative of velocity. a(t)=v'(t)
So for your problem you are looking for a(2π) = v'(2π)
𝑣(𝑡) = 𝑡3 − sin 𝑡 + 2
𝑣'(𝑡) = a(t) = 3𝑡2 − cos 𝑡
𝑣'(2𝜋) = a(2𝜋) = 3(2𝜋)2 − cos 2𝜋
𝑣'(2𝜋) = a(2𝜋) = 3(4𝜋2) -1 = 12𝜋2-1