The position of an object moving along a line is given by $p (t) = 7 t - cos (\frac{π}{3} t) + 2$ $p(t) = 7t - cos(( pi )/3t) + 2$ . What is the speed of the object at $t = 5$ $t = 5$ ?

Question

1443 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-22T09:40:41

The speed is $= 6.09 m s^{- 1}$ $=6.09ms^-1$

We need

$(cosx)'=-sinx$

The speed is the derivative of the position

$p(t)=7t-cos(pi/3t)+2$

$v(t)=p'(t)=7+1/3pisin(pi/3t)$

The speed at $t=5$ is

$v(5)=7+1/3pisin(5/3pi)$

$=7+pi/3*-sqrt3/2$

$=6.09ms^-1$

The position of an object moving along a line is given by p(t) = 7t - cos(( pi )/3t) + 2 p(t)=7t−cos(π3t)+2p(t) = 7t - cos(( pi )/3t) + 2 . What is the speed of the object at t = 5 t=5t = 5 ?