The velocity - time graph of a particle in one dimensional motion is shown in figure.

Which of the following formulae are correct for describing the motion of the particle over the time- interval `t _(1)` to `t _(2)` :
(a) `x (t _(2)) = x (t _(1)) +v (t _(2) - t _(1)) + ((1)/(2)) a (t _(2) - t _(1)) ^(2)`
(b) `v (t_(2)) = v (t_(1)) + a (t _(1)))//(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))`
(e) `x (t _(2))=x(t_(1)) + v _("average") (t _(2) - t _(1)) + ((1)/(2)) a _("average") (t _(2) -t _(1)) ^(2)`
(f)` c (t _(2)) - c (t _(1)) =` area under the v-t curve bonunded by the t -axis and the dotted line shown.

Explanation

Slope of graph is not constant during `t_(1)` to `t_(2)` and not uniform, it means acceleration is not uniform. Hence, (a), (b) and (e) are not correct. Because these are for uniformly accelerated motion. But equations (c), (d) and (f) are correct because these equations are for regular and irregular acceleration (both).