SOLUTION: The distance, in feet, that a certain object travels after t seconds is given by the function d(t)=a(t)+1/2bt2, where a and b are positive constants. Which of the following functio

1.  Let me start explaining that the condition is written incorrectly.


    The correct formula for the distance traveled is  d(t) = a*t + (1/2)*bt^2.

    instead of  d(t) = a(t) + (1/2)*b*t^2.


    (Since "a" is a constant, there is no sense to write a(t), presenting "a" as a function of "t".)




2.  Let me continue, stating that the optional answer list  DOES NOT CONTAIN the correct formula (!)


        (In other words, no one of the proposed options does fit as the correct answer.)




3.  Let me to explain you what happens in reality, from the Physics point of view.


    The given distance formula presents the distance at the uniformly accelerated rectilinear move.


    "a" is the initial velocity.  "b" is the acceleration.

    At such move, the velocity  is the linear function of time  v(t) = a + b*t.


    The arithmetic mean of the rate  is   = . 


    It is the correct answer.


    The average rate, calculated as the traveled distance divided by the time, is the same

          = .




4.  Final answer is  ,


    which is not in the list.