# A particle of mass 1kg moves in a straight line under the influence of a force, which increases linearly with the time at the rate of 60N

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A particle of mass 1kg moves in a straight line under the influence of a force, which increases linearly with the time at the rate of 60N per sec. At time t = 0 the initial force may be taken as 50N. Determine the acceleration and velocity of the particle 4sec after it started from rest at the origin.

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As the force varies linearly with time,

F = mt + C

Differentiate the equation with time

dF/dt = m = 60(given)

i.e., m = 60 ...(i)

Given that, at t = 0, F = 50N,

50 = 60 X 0 + C

C = 50 ...(ii)

Now the equation becomes,

F = 60t + 50 ...(iii)

Since, F = ma, m = 1Kg

F = ma = 1.a = 60t +50

At t = 4 sec,

a = 60 X 4 + 50 = 290

also, a = dv/dt

a = dv/dt = 60t + 50

Integration both side for the interval of time 0 to 4sec

V = (60t2 + 50t), limit are 0 to 4

V = 30(4)2 + 50 X 4

V = 680m/sec

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