Question

two particles A and B are separation of 0.1 KM they move towards each other with uniform speed 18 km per hour and 54 km per hour respectively where do the two particle meets

Answer 1

let they meet at a distance x from A

as time remains the same

so

X/18 = (0.1-x)/54. ( because total distance is 0.1 so distance from b = 0.1 -x)

54x = 1.8 - 18x

72 x = 1.8
x =1.8/72 = 0.4

Answer 2

Let t = time taken to meet each other

    x = distance traveled by A (see attachment)

    y = distance traveled by B = 0.1 -x

Now we can use a linear motion equation,

      S = ut + (1/2)at²----- (1)

For particle 'A',

      S = traveled distance = x

      U = initial velocity = 18 km/h

      a = acceleration = 0

Substituting above values for equation (1),

    x = 18t  

    t = x/18 -----(2)

For particle 'B,

      S = traveled distance = 0.1-x

      U = initial velocity = 54 km/h

      a = acceleration = 0

Substituting above values for equation (1),

    0.1-x = 54t  

    t = 0.1 -x/54 -----(3)

equaling equation (2) & (3),

    $x/18 = (0.1-x)/54\\ 54x = 18(0.1-x)\\ 54x = 1.8 -18x\\ 36x = 1.8\\ x = 0.05 km$

Answer: two particles meet at 0.05 km