Answer
$11.25~m$
Work Step by Step
At $t=0$, the car is at $x=15~m$ and the truck is at $x=-35m$. If the car and the truck are heading directly toward one another, the car must be traveling in the negative direction (negative velocity) while the truck must be traveling in the positive direction (positive velocity). So, the light green line belongs to the truck while the dark green line belongs to the car.
The truck: $x_0=-35~m$, $v_0=10~m/s$, $v=0$, $t=2.5~s$
$v_{av}=\frac{v_0+v}{2}=\frac{10~m/s+0}{2}=5~m/s$
$v_{av}=\frac{\Delta x}{\Delta t}$. Rearranging the equation:
$\Delta x=(v_{av})(\Delta t)=(5~m/s)(2.5~s)=12.5~m$
But, $\Delta x=x-x_0$
$12.5~m=x-(-35~m)$
$x=12.5~m-35~m=-22.5~m$
The car: $x_0=15~m$, $v_0=-15~m/s$, $v=0$, $t=3.5~s$
$v_{av}=\frac{v_0+v}{2}=\frac{-15~m/s+0}{2}=-7.5~m/s$
$v_{av}=\frac{\Delta x}{\Delta t}$. Rearranging the equation:
$\Delta x=(v_{av})(\Delta t)=(-7.5~m/s)(3.5~s)=-26.25~m$
But, $\Delta x=x-x_0$
$-26.25~m=x-(15~m)$
$x=-26.25~m+15~m=-11.25~m$
$Separation=x_{car}-x_{truck}=-11.25~m-(-22.5~m)=11.25~m$
