Calculating Particle Speed with Velocity-Dependent Force

[ssmooc]

A particle of mass m moving parallel to the x-axis is actuated by a speed-dependent force directed against its movement. The force is given by:

F → = -be ^ CV I

where b is a positive constant (N units), and IA also a positive constant (units of s-1 m) and v is the velocity, the magnitude of the particle velocity (unit m · s -1).

If t = 0, the particle moves with velocity v0. Find the speed v (t) as a function of time t. Express your answer in terms of some or all of the following: b, m, t, c, v0. Use ln () for the natural logarithm function and e ^ () to the exponential function, if necessary.

v (t) =?

2. Homework Equations

v (t) =

3. The Attempt at a Solution

v (t) = (v_0 * b * cos (* t v_0) v_0 * + C * cos (* t v_0))

 

[Chestermiller]

A particle of mass m moving parallel to the x-axis is actuated by a speed-dependent force directed against its movement. The force is given by:

F → = -be ^ CV I

where b is a positive constant (N units), and IA also a positive constant (units of s-1 m) and v is the velocity, the magnitude of the particle velocity (unit m · s -1).

If t = 0, the particle moves with velocity v0. Find the speed v (t) as a function of time t. Express your answer in terms of some or all of the following: b, m, t, c, v0. Use ln () for the natural logarithm function and e ^ () to the exponential function, if necessary.

v (t) =?

2. Homework Equations

v (t) =

3. The Attempt at a Solution

v (t) = (v_0 * b * cos (* t v_0) v_0 * + C * cos (* t v_0))

please show your working.