The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval `t_1` to `t_2`?

Options

A. `x(t_2) = x(t_1) + v(t_1)(t_2 - t_1) + (1/2)a(t_2 - t_1)^(2)`
B. `v(t_2) = v(t_1) + a(t_2 - t_1)`
C. `v_"average" = (x(t_2) + x(t_1))/(t_2 - t_1)`
D. `a_"average" = (v(t_2) - v(t_1))/(t_2 - t_1)`

Answer

D

Explanation

In the given interval the slope of v-t graph (i.e acceleration) neither constant nor unifrom. Therefore relations (a), (b) and (c ) are incorrect but (d) is correct.