A body of mass m rests on a smooth horizontal plane. At the moment t=0 a horizontal force is applied to it which varies with time applied F=at where a is constant. Find average force during first time secondsince after the force act.
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11th
Physics
Laws of Motion
Problems on Friction
A body of mass m rests on a...
PHYSICS
A body of mass m rests on a horizontal plane with a friction coefficient μ. At t=0, a horizontal force is applied (F=at) where a is a constant vector. Find the distance traversed in first t sec.
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ANSWER
Let at time t
0
the body begins to move. so, at
0
=μmg
or, t
0
=
a
μmg
now, m
dt
dv
=a(t−t
0
)
put t−t
0
=T
or, dv=
m
a
TdT
integrating both sides,v=
2m
aT
2
as v=
dt
dx
, so, x=∫
2m
aT
2
dT=
6m
aT
3
distance x=
6m
a
(t−
a
μmg
)
3
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