Question

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

Answer 1

Answer:- F = mg

Explanation:

Given that motion of particle is given by

y = ut+ 1/2 gt²

Differentiating the above equation with respect to t

dy/dt = u + 1/2(2gt)

dy/dt = u + gt

We know that dy/dt = v, where v is velocity of particle.

Thus,

v = u + gt

Again, Differentiating this expression with respect to t

dv/dt = 0 + g×1

dv/dt = g

We know that dv/dt = a, where a is acceleration of the particle.

Thus,

a = g

Now, We know that

Force(F) = Mass(m) × Acceleration (a)

F = m × a

F = m × g

F = mg

Note:- 1) Rate of change in displacement with respect to time is called 'Velocity', i.e.

dy/dt = v

2) Rate of change in velocity with respect to time is called 'Acceleration', i.e.

dv/dt = a