A block of mass 1 kg starts from rest at x = 0 and moves along the x - axis under the action of a force F = kt, where t is time and k = 1 N/s. The distance the block will travel in 6 seconds is

A block of mass 1 kg starts from rest at x = 0 and moves along the x -

1.	A block of mass 1 kg starts from rest at x = 0 and moves along the x - axis under the action of a force F = kt, where t is time and k = 1 N/s. The distance the block will travel in 6 seconds is
Answer» 36 m 72 m 108 m 18 m Solution :F = kt or , m`(DV)/(dt) = kt " " or, (dv)/(dt) = (k)/(m)`t or, `int_(0)^(v) = (k)/(m)int_(0)^(t)" "or, v = (1)/(2)(k)/(m)cdot t^(2) " " or, (dx)/(dt) = (1)/(2)(k)/(m)t^(2)` `or," " int_(0)^(x) dx = (1)/(2)(k)/(m)int_(0)^(6) t^(2) dt` `or," "x = (1)/(2)(k)/(m)(6^(3))/(3) xx (1)/(2)xx(1)/(1) xx (216)/(3) [ because k = 1 N//s, m = 1 kg]` = 36 m The option A is CORRECT.