Physics - Kinematics Question with Solution | TestHub

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

For $t=0$ to $t=20 \mathrm{s}$,

$a_1=\frac{20}{20} =1 \mathrm{m} {\mathrm{s}}^{-2}$

For $t=20 \mathrm{s}$ to $t \mathrm{s}$,

$a_2=\frac{0-20}{25-20}=-4 \mathrm{m} {\mathrm{s}}^{-2}$

  $0=\frac{1}{2}\times 20\times 25+\frac{1}{2}\times \left(-4\right)\times {\left(\text{t}-25\right)}^2$

$(t - 25{)}^2 = 125$
$t - 25 = \pm 11.2$

$t >25 \mathrm{s}$

$t = 36.2 \mathrm{s}$