Question

The position of an object moving along a line is given by `p(t) = 2t - sin(( pi )/6t)`. What is the speed of the object at `t = 16`?

Answer 1

The speed is `=2+pi/12`

Explanation:

If the position is `p(t)=2t-sin(pi/6t)`
Then the velocity is given by the derivative of `p(t)`
`:. v(t)=2-pi/6cos(pi/6t)`
When `t=16`
`v(16)=2-pi/6cos(pi/6*16)`
`=2-pi/6cos(8/3pi)=2-pi/6*(-1/2)`
`=2+pi/12`