The position of a particle moves along the equation X = Vo/K (1 - e^(-KT))

Question

Vo and K are constants
a)determine the total distance that the particle moves
b) Show that the aceleration is derived from the velocity
c) Reason how it could take an infinite amount of time to move a definite distance

Answer 1

a
as t --> oo, x --> Vo/k total distanced moved is Vo/k

b
v = (Vo/k)(ke^-kt) = Vo e^-kt
a = -Vo k e^-kt

c
as t gets large, velocity gets smaller and smaller and acceleration is always negative and also smaller and smaller.

Answer 2

Thank you!