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 = 24`?

Answer 1

`v` = `3.785` `m/s`

Explanation:

The first time derivative of a position of an object gives the velocity of the object
`dot p(t) = v(t)`
So, to get the velocity of the object we differentiate the position with respect to `t`
`p(t)=3t-2sin(pi/8t)+2`
`dot p(t)=3-2*pi/8*cos(pi/8t)=v(t)`
So speed at `t=24` is
`v(t)=3-pi/4cos(pi/8*24)` ;or
`v(t)=3-pi/4(-1)` ;or
`v(t)=3+pi/4=3.785` `m/s`
Hence the speed of the object at `t=24` is `3.785` `m/s`