In the figure here, a red car and a green car move toward each other in adjacent

Question

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 212 m. If the red car has a constant velocity of 28.0 km/h, the cars pass each other at x = 43.5 m. On the other hand, if the red car has a constant velocity of 56.0 km/h, they pass each other at x = 76.2 m. What is the initial velocity (in km/h) of the green car?

I'm stuck I've used every equation of the five and I just do not understand or comprehend at all.

Explanation / Answer

When velocity of red car, v = 28 km/hr = 28000/3600 = 7.78 m/s
Constant velocity implies acceleration = 0
So, v = distance travelled / time
time = distance / v = 43.5 / 7.78 = 5.59 sec

this is also the time green car travelled so that they meet each other at x = 43.5 m.
let us consider that the direction of red car is positive then the direction of green car will be -ve.
Now,
x - xo = ut + (1/2) at2 where a = acceleration of green car,

t = time both cars moved to meet each other at 43.5 m

u = inital velocity of green car.

43.5 - 212 = u * 5.59 + (1/2) a (5.59)2

-168.5 = 5.59 u + 15.62 a ------------------------(I)

Now, when velocity of red car, v = 56km/hr = 56000/3600 = 16.11 m/s

v = distance / time

time = distance / v = 76.2 / 16.11 = 4.73 sec

then, x - xo = ut + (1/2) at2

76.2 - 212 = u * 4.73 + (1/2) * a * (4.73)2

-135.8 = 4.73 u + 11.19 a ------------------------(II)

Equating eqn (I) and (II) , we get

[ -168.5 = 5.59 u + 15.62 a ] * 11.19 implies - 1885.51 = 62.55 u + 174.79 a

[ -135.8 = 4.73 u + 11.19 a ] * 15.62 implies - 2121.20 = 73.88 u + 174.79 a

hence, 235.69 = - 11.33 u

u = - 235.69 / 11.33 = - 20.80 m/s note -ve sign accounts for the opposite dirn relative to red car which we assumed to be positive.

substituting u in eqn (II) we get

-135.8 = 4.73 * (-20.80) + 11.19 a

-135.8 = - 98.38 + 11.19 a

a = - 37.42 / 11.19 = - 3.34 m /s2  

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