Question

determine the initial velocity and acceleration of a particle travelling with uniform acceleration in a straight line if it travels 55 m in the 8th second and 85 m in the 13th second ?

Answer 1

The distance traveled by a particle during the  nth second is given by
             Sn = u + (n-1/2) a            u = initial velocity, a = acceleration

55 = u + (8 - 1/2) a            - distance traveled in 8th second

           u + 15a /2  = 55  --- equation 1

           u + 25a/2 = 85 --- equation 2        - distance traveled in 13th second

Let us subtract eq 1 from eq 2
10a/2 = 30                        a = 6 m /sec²

u + 15*6/2 = 55                u = 55-45 = 10 m/sec