Question:
At the instance the traffic light turns green, an car starts with constant acceleration a of 2. m/sec2. At the same instant a truck, traveling with constant speed of 100 km/h , over takes and passes the car. How far beyond the traffic signal will the car overtake the track?

 

Answer:

Since the final velocity of the car is missing, Eq. (2):

,

can be used to solve this question.

 

Assume the traffic light is at x0=0 and  the car meets the truck at x.

Applying this equation to the truck (the truck has zero acceleration), we get


x=vtr t,                                              (a)
where vtr is the speed of the truck.

Applying Eq(2) to the car (the car starts from rest), we get

x =0.5  a t2                                                (b).

We have two equations and two unknowns, namely, t and x.  We should be able to solve for these two unknown.

 

x = 0.5 a (x/vtr)2.

or

x =Sqrt(2/a) vtr

we need to convert the speed of the truck to the m/s unit,

vtr= 100 km/h = 27.8 m/s.

 

x =Sqrt(2/2.0) 27.8 = 27.8 m.