To solve this problem it is necessary to apply the concepts related to the concept of overlap and constructive interference.
For this purpose we have that the constructive interference in waves can be expressed under the function

Where
a = Width of the slit
d = Distance of slit to screen
m = Number of order which represent the number of repetition of the spectrum
Angle between incident rays and scatter planes
At the same time the distance on the screen from the central point, would be

Where y = Represents the distance on the screen from the central point
PART A ) From the previous equation if we arrange to find the angle we have that



PART B) Equation both equations we have


Re-arrange to find a,


Answer:


Δd = 
Explanation:
As
, when the car is making full stop,
.
. Therefore,

Apply the same formula above, with
and
, and the car is starting from 0 speed, we have

As
. After
, the car would have traveled a distance of

Hence 
As
we can simplify 
After t time, the train would have traveled a distance of 
Therefore, Δd would be 
You draw a straight line from the start point to the end point. It doesn't matter what route was actually followed for the trip.