I have trouble understanding the following problem's answer:
Which of the following relations are true for any arbitrary motion in space?
(a) $v_{avg}=\frac{r(t_2)-r(t_1)}{t_2-t_1}$
(b) $v_{avg}=\frac{v(t_1)+v(t_2)}{2}$
(c) $a_{avg}=\frac{v(t_2)-v(t_1)}{t_2-t_1}$
Clearly b is wrong.
But my book says a and c are correct:
avg velocity=total distance by total time, so, how is the first part taking out total dist / total time? I would think
$$v_{avg}=\frac{v_1(t_1)+v_2(t_2)}{t_1+t_2}$$
and similarly for avg acceleration. Why isn't this the case?