A particle is moving along X -axis with velocity v=e^ - x . At time t=0 , the particle is located at x=0 . The displacement of the particle as function of time is

Step-by-step solution

Velocity of particle, v=e^ - x d x d t =e^ - x or d x e^ - x =d t or e^ x d x=d t Integrating, we get ₀^x e^ x d x= ₀^t d t aligned & 1 [e^ x ]₀^x=[t]₀^t & 1 (e^ x -e^0 )=t-0 1 (e^ x -1 )=t aligned e^ x = t+1 Taking log, we get (e^ x )= ( t+1) array ll & x= ( t+1) & x= 1 ( t+1) array So, displacement function for the particle is x= 1 ( t+1)