How to approach this question using SUVAT equations?

[Physical_Fire]

Homework Statement

A car X is travelling at a constant speed u along a straight road. At time t = 0 a second car Y is a
distance d0 behind car X and travelling at a speed v in the same direction. Speed v is less than
speed u

Relevant Equations

S= ut+(1/2) at^2

Hello,
I came across the question attached. To approach this, I assigned S1 to car X and S2 to car Y. So the displacement of Car X is S1=S2 + d(naught). Then using S1= ut+(1/2) at^2 for car X and S2= uT , I got to uT + d(naught) = VT + (1/2)aT^2. However, I am stuck here as I can't relate distance with time as per the graphs. Any nudge in the right direction is appreciated.

Thanks.

 

[PeroK]

The question asks for the distance between cars X and Y. That's $S_1 - S_2$

 

[Physical_Fire]

So i get s1-s2=UT-VT-(1/2)aT^2. I still cant see the relation

 

[Steve4Physics]

To approach this, I assigned S1 to car X and S2 to car Y. So the displacement of Car X is S1=S2 + d(naught). Then using S1= ut+(1/2) at^2 for car X and S2= uT , I got to uT + d(naught) = VT + (1/2)aT^2. However, I am stuck here as I can't relate distance with time as per the graphs. Any nudge in the right direction is appreciated.

It may be worth noting that the question can be solved without any equations - just using some careful thinking. (Perhaps you've already done that.) That's probably the approach intended by the question's author.

Of course, solving it using suvat equations is perfectly viable and is a valuable learning-experience.

 

[PeroK]

So i get s1-s2=UT-VT-(1/2)aT^2. I still cant see the relation

Choose some possible values for $u, v$ and $a$ and draw a graph of that function.