Answer:
The equation that represents the instantaneous velocity at any given time, t is:
[tex]v (t) = 8t -2[/tex]
Step-by-step explanation:
In physics, the equation that describes the instantaneous velocity of an object is the derivative of the position of this object as a function of time.
In this problem we have the function that describes the position of the object at a time t.
[tex]f (t) = 4t ^ 2-2t[/tex]
Therefore to obtain the instantaneous velocity we derive f (t) with respect to time
[tex]\frac{df(t)}{dt} = 2(4)t-2\\\\\frac{df(t)}{dt} = 8t-2 = v (t)[/tex]
Finally the equation of velocity is:
[tex]v (t) = 8t -2[/tex]
