Finding the acceleration of a particle given the function

Question

The velocity of a particle at time t is given by the function 𝑣(𝑡) = 𝑡³ − sin 𝑡 + 2, what is the acceleration of the particle at time 𝑡 = 2𝜋?

Answer 1

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