Question

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

Answer 1

y = ut + 1/2 gt2

dy/dt = d/dt ut + d/dt 1/2 gt2

v= u + 2gt

dv/dt = d/dt u + d/dt 2gt

a = 0 + 2g

a = 2g

acceleration of particle =a =2g

mass of particle = m [Given]

Force = mass * acceleration

F = m * 2g

F = 2gm

(The derivative of g*t^2 is g*2t)
it is done by the equation
d/dx(x^n) = nx^(n-1)

here,

d/dt(t2) = 2t^(2-1)
=2t