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 $t = 7$ ?

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Answer 1 · 2017-07-15T14:23:49

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

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.

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