# Motion in 1-D problem!

## Homework Statement

A huge tractor and a Tesla full of school children come driving along a winding
mountain road, in opposite directions. The tractor has a speed of 40:0km/h
and the car zooms along with 80:0 km/h. The Tesla suddenly comes around a
corner, sees the tractor, and they both immediately start braking, both with
constant accelerations of 5:00 m/s2 (opposite to their directions of motion).

a) If the initial distance between the two is 60:0 m, do they hit each other? If
so, where, and with what relative speed on impact? If not, what is the distance
between the two when they both stop?

In fact, it takes both of them 0:50 s to react to seeing each other, so they only
start braking 0:50s after the car comes round the corner.
b) What is the answer to the questions in a) in this case?

As it happens the tractor driver is looking the other way, and doesn’t brake
at all, but continues with his original speed.
c) What should the acceleration a of the Tesla be, to have time to stop before
being hit by the tractor (still including the 0.5 s delay from question b))?

## Homework Equations

(1) Vf=Vi+at
(2) s=Vi*t+0.5at^2
(3) s=0.5(Vi+Vf)*t
(4) 2as=Vf^2-Vi^2

## The Attempt at a Solution

By eq 4 s=Vi^2/(2a) the tractor travels 12,35m and the Tesla 49,38m, and so there would be an impact.
The Tesla uses 4,44 seconds to brake until rest, and the tractor uses 2,22 seconds.

So I was thinking that I could describe each of their paths by eq 2, putting my coordinate system at the tractor for t=0. Then their paths would be:(Note, they both have same acceleration, and the Tesla moves at double speed of the tractor.)
For Tesla: S1= -2Vi+0.5at^2+60m
For tractor: S2= 2Vi-0.5at^2

So I was thinking S1=S2 would give me the time of impact, and then I could calculate each speed by Vf=Vi-at.
But after doing this I keep on getting the wrong answer... :(