[tex]S=ut+\frac{1}{2}at^2[/tex]
First [tex]10[/tex] seconds :
At [tex]t=0[/tex], the velocity of particle is [tex]0[/tex] as it is starting from rest. Therefore, [tex]u=0[/tex] and the distance travelled is given by
[tex]X=0*10+\frac{1}{2}a*10^2=50a[/tex]
Next [tex]10[/tex] seconds :
By the end of [tex]10[/tex]th second, the particle's velocity reaches [tex]10a[/tex]. Therefore, [tex]u=10a[/tex] and the distance travelled is given by
[tex]Y=10a*10+\frac{1}{2}a*10^2=150a[/tex]
Dividing gives
[tex]\frac{Y}{X}=\frac{150a}{50a}=3[/tex]
[tex]\implies\boxed{Y=3X}[/tex]
