Question

The position of an object moving along a line is given by `p(t) = cos(t- pi /3) +1`. What is the speed of the object at `t = (2pi) /4`?

Answer 1

`v((2pi)/4) = -1/2`

Explanation:

Since the equation given for the position is known, we can determine an equation for the velocity of the object by differentiating the given equation:

`v(t) = d/dt p(t) = -sin(t - pi/3)`

plugging in the point at which we want to know speed:
`v((2pi)/4) = -sin((2pi)/4 - pi/3) = -sin(pi/6) = -1/2`

Technically, it might be stated that the speed of the object is, in fact, `1/2`, since speed is a directionless magnitude, but I have chosen to leave the sign.