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?
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.
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.