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Class 11
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>>Work Done by a Variable Force
>>A time dependent force F = 6t acts on a
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A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from set, the work done by the force during the first 1 sec. will be :
Medium
Solution
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Correct option is D)
Given,
F=6t
m=1kg
Force, F=ma=6t
1×
dt
dv
=6t
dv=6tdt
Integrating both side,
v=∫dv=∫
0
1
6tdt
v=6[
2
t
2
]
0
1
v=3m/s
Initial velocity, u=0m/s
From work energy theorem,
W=K
f
−K
i
W=
2
1
mv
2
−
2
1
mu
2
W=
2
1
×1×3×3−
2
1
×1×0×0
W=4.5−0=4.5J