Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag = kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity v0. To solve for the position as a function of time x(t), construct the net force in the x-axis. Further, employ the rules of integration results to the following expression for position as a function of time. To solve for the velocity as a function of position v(x), we construct the net force in the x-axis, then, eliminate time by expressing, the velocity on the left side of the equation. By integrating and applying the limits, we then shall arrive with a velocity that decreases in a linear maner.
Problem
Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as
Fdrag = kmv
where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity v0.
To solve for the position as a function of time x(t), construct the net force in the x-axis.
Further, employ the rules of integration results to the following expression for position as a function of time.
To solve for the velocity as a function of position v(x), we construct the net force in the x-axis, then, eliminate time by expressing, the velocity on the left side of the equation.
By integrating and applying the limits, we then shall arrive with a velocity that decreases in a linear maner.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 13 images
