
A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at `x=0`, its velocity at `x=12m` is
A. `4sqrt5m//s`
B. `20sqrt2m//s`
C. `20sqrt3m//s`
D. `40m//s`
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Correct Answer – D
(d) Area between curve and displacement axis
=`(1)/(2) xx (12 + 4) xx 10 = 80 J`
In this time the body acquired kinetic energy `= (1)/(2) mv^2` by the law of conservation of energy
`(1)/(2) mv^2 = 80 J`
`rArr (1)/(2) xx 0.1 xx v^2 = 80`
`rArr v^2 = 1600`
`rArr v = 40 m//s`.
Correct Answer – D
`x=0` to `x=12m`
`W=`area of F-x graph
`=(1)/(2)(4+12)xx10=80J`
`x=0`,`K_1=0`
`W=K_2-K_1`
`80=(1)/(2)mv^2-0=(1)/(2)xx0.1v^2`
`v^2=1600impliesv=40(m)//(s)`
Correct Answer – D
Correct Answer – D