Displacement(x) of a moving body changes with time(t) as x^2=t^2+2t+3 . Then find the relation between displacement(x) and acceleration(a) of this body?

1 Answer
Jul 31, 2017

Given relation between displacement #x# and time #t#
#x^2=t^2+2t+3#
acceleration #a=(d^2x)/dt^2#

First differential
#d/dtx^2=d/dt(t^2+2t+3)#
#2x(dx)/dt=(2t+2)#
#x(dx)/dt=t+1#

Differentiating again
#d/dt(x(dx)/dt)=d/dt(t+1)#
#x xxa+(dx)/dt(dx)/dt=1#
#=>a=(1-((dx)/dt)^2)/x#
can also be written as
#=>a=(1-(dotx)^2)/x#

Is the required expression.