Question

The position of an object moving along a line is given by `p(t) = 7t - cos(( pi )/3t) + 2`. What is the speed of the object at `t = 8`?

Answer 1

`7.907 m/s`

Explanation:

Speed is the magnitude of velocity. Velocity is the change in position. `p'(t)=v(t)`

`p(t)=7t-cos(pi/3t)+2 => p'(t)=v(t)=7+pi/3sin(pi/3t)`

at `t=8` we have `v(8)=7+pi/3sin(pi/3(8))=7+pi/3sin((2pi)/3)=7+pi/3(sqrt(3)/2)=7+(sqrt(3)pi)/6approx7.907m/s`