The figure shows the v - t graph of a particle moving in a straight...

For a particle to return to origin. Net displacement is zero.
 

For $t = 0$ to $t = 20s$,

${a}_{1} = \dfrac{20}{20} = 1m{s}^{- 2}$

For $t = 20s$ to $ts$,

${a}_{2} = \dfrac{0 - 20}{25 - 20} = - 4m{s}^{- 2}$

  $0 = \dfrac{1}{2} \times 2 0 \times 2 5 + \dfrac{1}{2} \times \left(- 4\right) \times {\left(\text{t} - 2 5\right)}^{2}$

$( t - 25{)}^{2} = 125$
$t - 25 = \pm 11 . 2$

$t > 25s$

$t = 36 . 2s$