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" Ns"^(-1)`. The distance, the block will travel in 6 seconds is

Options

A. 36m
B. 72m
C. 108m
D. 18m

Answer

A

Explanation

Block of mass 1kg moves along x axis under a force F=kt
`therefore F=ma=kt`
`implies 1 times (dv)/(dt)= kt `
By integrating both sides, we get
`v=(kt^2)/2 or (dx)/(dt)=(kt^2)/2`
Again by integrating both sides, we get
`therefore x=t^3/6`
As t=6s, `x=(6)^3/6=36m`