Question

The position of an object moving along a line is given by `p(t) = 3t - 2sin(( pi )/8t) + 2`. What is the speed of the object at `t = 12`?

Answer 1

I found: `3m/s`

Explanation:

We can find the instantaneous speed by deriving with respect to `t` and evaluate the derivative at `t=12`:
`s(t)=p'(t)=(dp(t))/(dt)=3-2pi/8cos(pi/8t)+0=`
`=3-pi/4cos(pi/8t)`

at `t=12`
`s(12)=3-pi/4cos(pi/8*12)=3+0=3m/s`