Answer
56.6 s
Work Step by Step
Recall the kinematic equation
$x= x_{0}+ v_{0}t+ \frac{1}{2}at^{2}$
Using this equation, for the first $\frac{1}{4}$ of the distance, we have
$\frac{900\,m}{4}=0+0\times t+\frac{1}{2}\times2.25\,m/s^{2}\times t^{2}$
$\implies\, 225\,m=1.125\,m/s^{2}\times t^{2}$
Or $t=\sqrt {\frac{225\,m}{1.125\,m/s^{2}}} =14.142 s$
At this time, velocity= u+at= $2.25\,m/s^{2}\times14.142\,s=31.82\,m/s$
For the remaining $\frac{3}{4}$ of the distance,
$v=0, v_{0}= 31.82\,m/s$ and $a=-0.750\,m/s^{2} $
t is obtained using the equation $v=v_{0}+at$.
$0= 31.82\,m/s+(-0.750\,m/s^{2})t$
Or $0.750\,m/s^{2}\times t= 31.82\,m/s$
$\implies\, t=\frac{31.82\,m/s}{0.750\,m/s^{2}}=42.43\,s$
Total travel time= $14.142\,s+42.43\,s=56.6\,s$
