Question

please solve with complete steps

Answer 1

The equation of displacement is given as:
$x- x_{o} =ut+ \frac{1}{2} w t^{2}$
where, 
$x_{o}$: position at time t=0s
u: initial velocity of particle or velocity at time t=0s
t: instant of time
w: acceleration of particle
Initial velocity of particle is 0 m/s therefore equation reduces to
[tex]x- x_{0} = \frac{1}{2}w t^{2} [/tex]

At t=n 
$b-a= \frac{1}{2}wn^2$
At t=2n
$c-a= \frac{1}{2}w(2n)^2=2wn^2$

$Therefore, b= \frac{1}{2}wn^2+a \\ 2b=wn^2+2a...(1) \\ c=2wn^2+a...(2) \\ Eq(2)-Eq(1): \\ c-2b=wn^2-a \\ w= \frac{c-2b+a}{n^2}$