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A time dependent force F=6t acts on a pa...

A time dependent force `F=6t` acts on a particle of mass `1kg`. If the particle starts from rest, the work done by the force during the first `1 sec.` will be

A

18J

B

4.5J

C

22J

D

9J

Text Solution

Verified by Experts

The correct Answer is:
B
`a= (F)/(m)= (6t)/(1)= 6t`
`(dv)/(dt)= 6t, dv= 6t dt`
`underset(0)overset(v)int dv= 6 underset(0)overset(1)int t dt`
`v= 6 [(t^(2))/(2)]_(0)^(1)=3`
`W= Delta KE= K_(F)- K_(i)= (1)/(2) (1)(3)^(2)= 4.5J`
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