For any arbitrary motion in space,which of the following relations are true?
$(a)$ $v_{\text{average}} = (1/2) (v(t_1) + v(t_2))$
$(b)$ $v_{\text{average}} = [r(t_2) - r(t_1)] / (t_2 - t_1)$
$(c)$ $v(t) = v(0) + at$
$(d)$ $r(t) = r(0) + v(0)t + (1/2)at^2$
$(e)$ $a_{\text{average}} = [v(t_2) - v(t_1)] / (t_2 - t_1)$
(The 'average' stands for the average of the quantity over the time interval $t_1$ to $t_2$.)

(B, E) False: This relation holds only for uniform acceleration. For arbitrary motion,it is not generally true.
$(b)$ True: By definition,average velocity is the total displacement divided by the total time interval.
$(c)$ False: This equation is valid only for constant acceleration. In arbitrary motion,acceleration is not necessarily constant.
$(d)$ False: This is the kinematic equation for constant acceleration. It does not apply to arbitrary motion.
$(e)$ True: By definition,average acceleration is the change in velocity divided by the time interval over which the change occurs.