Aparticle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. what is the acceleration of the particle at time t = 0 seconds?

The acceleration of the particle at time t = 0 seconds is:

                       4  feet per square  second.

                         i.e.   4 ft/s²

We are given a position function in terms of the time t as:

Now, we are asked to find the acceeleration of the particle at time t = 0 seconds.

We know that the acceleration of a particle is given by:

where v is the velocity of the particle which is calculated by:

Hence, we get:

i.e. the acceleration of the particle is the double derivative of the position.

and

i.e.