Answer
$x_{1}=1.5\space km,\space x_{2}=0.5\space km$
Work Step by Step
Here we use equation 2.9, $V^{2}=u^{2}+2aS$ to find the $x_{1},x_{2}.$
Let's apply this equation to the first phase of the trip.
$V^{2}=u^{2}+2aS$
$V^{2}=0^{2}+2a_{1}x_{1}$
$x_{1}=\frac{V^{2}}{2a_{1}}-(1)$
Let's apply this equation to the second phase of the trip.
$V^{2}=u^{2}+2aS$
$0^{2}=V^{2}+2a_{2}x_{2}$
$x_{2}=-\frac{V^{2}}{2a_{2}}-(2)$
$a_{2}=-3a_{1}=\gt (2)$
$x_{2}=\frac{V^{2}}{6a_{1}}-(3)$
$(1)\div (3)$,
$\frac{x_{1}}{x_{2}}=\frac{(\frac{V^{2}}{2a_{1}})}{(\frac{V^{2}}{6a_{1}})}=3$
$x_{1}=3x_{2}-(4)$
Total distance traveled by the cab driver $=x_{1}+x_{2}=2\space km$
(4)=>
$3x_{2}+x_{2}=2\space km$
$x_{2}=0.5\space km$
So, $x_{1}=1.5\space km$
