Aparticle of mass m sits at rest at x = 0. at time t = 0 a force given by f = fe^(-t/t) is applied in the +x direction; f and t are constants. when t = t the force is removed. at this instant when the force is removed, (a) what is the speed of the particle and (b) where is it?

Explanation:

Given:

Solving for :

where:

Integrating to get with initial conditions :

Integrating to get x with initial conditions x(0) = 0:

When t=T:

2.54 seconds

Explanation:

Gathering the data:

let molecular weight = 152 g/mol

diffusion coefficient = 0.114 cm²/s

Distance = 3 meters

The most important thing to know is Fick's Law of diffusion. The law states that the flux is directly proportional to the concentration gradient. In other words

where dc = change in concentration

            D = diffusion coefficient

            Dx = change in the distance, cm

solving:

j = dc/3 (-0.114)

 this gives t = 2.54 seconds