The position of an object moving along a line is given by p(t) = 2t - 2sin(( pi )/8t) + 2 . What is the speed of the object at t = 12 ?

1 Answer
Nathan L.
May 24, 2017

2.0 "m"/"s"

Explanation:

We're asked to find the instantaneous x-velocity v_x at a time t = 12 given the equation for how its position varies with time.

The equation for instantaneous x-velocity can be derived from the position equation; velocity is the derivative of position with respect to time:

v_x = dx/dt

The derivative of a constant is 0, and the derivative of t^n is nt^(n-1). Also, the derivative of sin (at) is acos(ax). Using these formulas, the differentiation of the position equation is

v_x(t) = 2 - pi/4 cos(pi/8 t)

Now, let's plug in the time t = 12 into the equation to find the velocity at that time:

v_x(12"s") = 2 - pi/4 cos(pi/8 (12"s")) = color(red)(2.0 "m"/"s"

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