Question

the motion of a particle of mass m is described by y=ut+1/2gt^2.find the force acting on particle.
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Answer 1

y = ut + ½ gt2

Differentiate y with respect to t which gives velocity as dy/dt = v

dy/dt = u + ½ g (2t)

v=u + gt -------------------Eqn (1) 

Differentiate v with respect to t which gives velocity as d2y/dt2 = dv/dt = a

dv/dt = 0 + g

a = g  ----------------------Eqn (2)

We know that force acting on a mass m is given by F = ma

Now from Eqn (2), substitute a =g, Hence, F = mg

Answer 2

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✍$<b>$
We have
$y = ut + \frac{1}{2} gt ^{2}$

velocity,
$v = \frac{dy}{dt} = u + gt$

Acceleration,
$a = \frac{dv}{dt} = g$

Force, F= ma=mg

Thus the given equation describes the motion of a particle and acceleration due to gravity and y is the position co-ordinate in the direction of g.

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