A particle ( m = 1 kg ) moves on the x axis. The initial position is x = 0 and the initial velocity is v(0) = 5 m/s. The particle experiences a force,
F(v,t) = − βv^2 e^(−αt)
(a) Determine the final velocity of the particle.
(b) Determine the distance it has moved at t = 10 seconds.
[DATA: α = 0.27 s−1 ; β = 1.19 kg/m .]
The Attempt at a Solution
This is part of the calculus review of my physics homework. What is confusing me is the function which is dependent on two variables.
For part (a) I divided the F function by the mass 1 kg which should then mean that a(v,t)=F(v,t)/m, correct? Beyond that I'm not sure how to differentiate the acceleration function to get velocity. If I differentiate with respect to t or with respect to v I still have a v in the equation which means I cannot find the limit of the resulting function as t approaches infinity to find the final velocity.
Once I figure out how to find the acceleration function I can probably differentiate that to find the position function for part (b).
Any suggestions? Thank you!