The driver knows that the beginning of the intersection is a distance X away, an

Question

The driver knows that the beginning of the intersection is a distance X away, and that the light
will turn green again in time tg. so he decides instead to put on his brakes and slow down such that he
arrives, car still moving, at the intersection just as the light is turning green.
a) Derive an expression for the speed the car will have when it gets to the intersection.
b) Derive an expression for the constant acceleration necessary for the car to accomplish this feat.
c) Calculate answers to the above if the intersection is 95meters away and the light will be turning green in 11.9seconds.

Explanation / Answer

a) let v be the speed of the car at the intersection

and u be the initial speed of the car before slows down and a be the accelaration

v = u - (a*tg)
and also v = sqrt(u^2-(2*a*X))

v^2 = u^2-(2*a*X)

v^2 = v^2+(2*v*(a*tg))+(a*tg)^2 -(2*a*X)

2*v*tg+(a*tg^2)-2X = 0

2*v*tg = 2x-(a*tg^2)

v = (x/tg)-(0.5*a*tg)

--------------------------------------

B) a = (v^2-u^2)/(2*X)

C) we must know some of the values to solvethe problem

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