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A block of mass 1 kg starts from rest at...

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

36 m

B

72 m

C

108 m

D

18 m

Text Solution

Verified by Experts

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.
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