The force acting on a particle of mass m is given by
f=kvx
in which k is a positive constant. the particle passes
throughthe origin with speed vo at time t=0. find x as a function
oft.

Answer with Explanation:

From newton's second law the acceleration produced by a force on a mass 'm' is given by

Applying the given values in the above equation we get

Also we know that acceelration of a particle can ve mathem,atically written as

Applying the given values in the above equation we get

'c' is the constant of integration

whose value is found that at x =0 v=

Thus

Thus the velocity as a function of position is

Now  by definition of velocity we have

Using the function of velocity in the above relation we get

where

is constant of integration

Now it is given that at t = 0 ,x = 0

thus from the above equation of position and time we get

Thus the position as a function of time is

where c=

fanswer:

explanation:

f