A body moving with uniform acceleration travels 24m in 6th second and 44m in 11th second. Find the :
(1) acceleration
(2) the initial velocity of the body?
Equations are to be used " S = u × t + (1/2) × a × t2 " 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 6th second: u5+(1/2)a = 24 …(1)
where u5 is speed after 5 seconds and is given by, u5 = u0 + 5a …(2)
where u0 is initial velocity. Using equations.(1) and (2) we can write u0 + (11/2) × a = 24 …(3)
44 m traveled in 11th second: u10 + (1/2)a = 44…(4)
where u10 is the speed after 10 seconds and is given by u10= u0 + 10a …(5)
using equations(4) and (5), we can write u0 + (21/2)a = 44 …(6)
Solving equations (3) and (6) , we get a = 4 m/s2 and u0 = 2 m/s