How to solve

$($I$)$ Time$-$Space analysis

$25$

I$($a$).$ Explain the diagram below I$($b$).$ perform an analysis, and I$($c$)$ mention uses of similar diagram and analysis mentioned in I $($a$).$ & I $($b$).$ in traffic enginecring.

Marks: $10+10+5]$ I$($a$).$

maths problem

$U_1=72,U_2=13s$

$T_3=15$

I$($b$).$ Three vehicles are travelling from Walsall to Wolverhampton in a morning peak hour. i Vehicle A starts the trip from the origin at $15$:$00$ with a constant speed of $U_{1}k\frac{m}{h}.$ After $T_1$ minutes, it stops at a parking bay and waits for $25$ minutes. It then performs a U $-$turm and travels towards the origin with a speed of $U_{2}k\frac{m}{h_3}$ Vehicle B departs from the origin $T_2$ minutes after $15$:$00,$ travelling with a constant speed of $U_{3}k\frac{m}{h}.s$ Vehicle C commences its trip from the origin $T_3$ minutes later than vehicle A with a constant speed $U_c.$

Draw a space$-$time diagram that illustrates the trajectory of the three vehicles.

Calculate the distance and point in time where vehicle $B$ will catch up with vehicle $A.$

Calculate the point in time where vehicle A and vehicle C will meet, in order to cross paths at $35$ km from the origin.

Calculate the speed $U_C$ that vehicle C was travelling, when it met vehicle A at $35$ km from the origin.

$[$Mark Distribution: $2\mathrm{.}54]$