Question:

At the instance the traffic light turns
green, an car starts with constant acceleration a of 2. m/sec^{2}.
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?

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

,

can be used to solve this question.

Assume the traffic light is at x_{0}=0 and the
car meets the truck at x.

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

x=v_{tr}
t,
(a)

where v_{tr} is the speed of the truck.

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

x =0.5 a t^{2
(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/v_{tr})^{2}.

or

x =Sqrt(2/a) v_{tr}

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

v_{tr}= 100 km/h = 27.8 m/s.

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