# A body moving with constant acceleration | travels the distance 3 metre and 8 metre respectively in 1 second and 2 second | calculate the initial velocity and the acceleration of body | Sum Motion in one Dimension - Physics class 9

Problem : A body moving with constant acceleration travels the distance 3 metre and 8 metre respectively in one second 2 second. Calculate the 1) initial velocity and 2) the acceleration of body. Data given: Distance( s 1 ) = 3m Time taken ( t 1 ) to travel 3 m =1 second Distance( s 2 ) = 8m Time taken ( t 2 ) to travel 8 m =2 second Initial velocity ( u )= ? Acceleration ( a ) = ? Case 1: We know s = ut + 1/2 a. t 2 Or s 1 = ut 1 + 1/2 a. t 1 2 or 3 = u . 1 + 1/2 .a . 1 2 or 3 = u + a/2 -------Eqn. 1 Case 2: s 2 = ut 2 + 1/2 a. t 2 2 or 8 = u . 2 + 1/2 .a . 2 2 or 8 = 2u + 2a or 8/2 = (2u + 2a)/2 or 4 = u + a -------Eqn. 2 Subracting Eqn. 1 from Eqn. 2 (Eqn. 2 - Eqn. 1) We have: 4 - 3 = (u + a) - (u + a/2) Or 1 = u + a - u - a/2 Or 1 = a - a/2 Or 1 = (2a - a)/2 Or 1 = a /2 Or a = 2 m/s 2 Putting the value of a in Eqn. 1 we have: 3 = u + 2/2 3 = u + 1 Or u = 3 - 1 Or u = 2 m/s ∴ Initial velocity ( u )