Given that

$a=-0.05v^2 --------- (i)$

We know that,

$v=\dfrac {dx}{dt} \\ a=\dfrac {dv}{dt} \\ \therefore \dfrac va= \dfrac {dx}{dv} \\ \therefore \dfrac {vdv}{dx}=a \\ \therefore \dfrac { vdv}{dx}=-0.05v^2 \\ \therefore dx=-\dfrac {dv}5 = -\dfrac {20 dv}v ------------(ii)$

At v=20m/s, x=0. Hence x at 15m/s is given by

$ x=-∫\limits_{20}^{15}\dfrac …