A body moving with uniform acceleration travels 24m in 6^{th} second and 44m in 11^{th} second. Find the :

(1) acceleration

(2) the initial velocity of the body?

Equations are to be used " S = u × t + (1/2) × a × t^{2} " and " v = u + a×t " .

u and v are initial and final velocity respectively. a is acceleration, S is the distance traveled and t is time.

24 m traveled in 6^{th} second: u_{5}+(1/2)a = 24 …(1)

where u_{5} is speed after 5 seconds and is given by, u_{5} = u_{0} + 5a …(2)

where u_{0} is initial velocity. Using equations.(1) and (2) we can write u_{0} + (11/2) × a = 24 …(3)

44 m traveled in 11^{th} second: u_{10} + (1/2)a = 44…(4)

where u_{10} is the speed after 10 seconds and is given by u_{10}= u_{0} + 10a …(5)

using equations(4) and (5), we can write u_{0} + (21/2)a = 44 …(6)

Solving equations (3) and (6) , we get a = 4 m/s^{2} and u_{0} = 2 m/s