A particle of mass 1 kg has potential energy, P.E, = 3x + 4y. At t = 0, the particle is at rest at (6, 4). Work done by external force to displace the particle from rest to the point of crossing the x axis is
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The particle was initially at rest at (6, 4)
∴ ∴ x = 6 + 
a x t 2
and y = 4 + 
a y t 2 ………….. (i)
Acceleration
i.e.,
a = (3 2 + 4 2 ) 1/2 = 5 ms -2 ………… (ii)
Substituting the value of a from (ii) in (i)
x = 
and y = (4 – 2t 2 )
Now y = 0 when particle crosses x – axis
∴ ∴ t = 
Displacement S = 
at 2
= 
= 5m
Then work done = F.S. = 5 × 5 = 25 J
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