Question

The position of an object moving along a line is given by `p(t) = 2t - cos(( pi )/6t)`. What is the speed of the object at `t = 7`?

Answer 1

`v = 1.74` `"LT"^-1`

Explanation:

We're asked to find the speed of an object moving in one dimension at a given time, given its position-time equation.

We therefore need to find the velocity of the object as a function of time, by differentiating the position equation:

`v(t) = d/(dt) [2t - cos(pi/6t)] = 2 + pi/6sin(pi/6t)`

At time `t = 7` (no units here), we have

`v(7) = 2 + pi/6sin(pi/6(7)) = color(red)(1.74` `color(red)("LT"^-1`

(The term `"LT"^-1` is the dimensional form of the units for velocity (`"length"xx"time"^-1`) . I included it here because no units were given.