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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))
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))