a train takes 50 seconds in going from station a to b and in going from b to another station c also it takes 50 seconds. the distance between a and b is   1 / 2 km and dist. between b and c is 3 / 4 km .if the accleration is uniform, find its magnitude. find also the velocities at a , b and c.

(dont only tell the answer but also specify how to solve it. i will be thankful to u ) 

1/2 km = 500m,  3/4 km = 750 m.

 

From question,

     500 = 50.u_a + 1/2. a. 2500

 or 500 = 50.u_a + 1250a ...................eq(1)

  u_b = u_a + 50a

Also,

  750 = 50u_b+ 1/2.a.2500

 750  = 50u_a + 2500a + 1250a ........................eq(2)

 

 (1) and (2) are the two equations in two unknowns u_a and a. Solve them to get the ans

 

When the train reaches station b then its velocity is u_b. So, in the journey from b to c the initial velocity of the train is u_b.

   Putting it in kinematic equation s = ut + 1/2 a t²

we have    750 = u_b.50 + 1/2. a. 2500

  But from kinematic equation v=u+at we have u_b= u_a+ a.50. Replace this value for u_b in the above equation to get eq (2)