Say there is a particle moving at $50~\text{m/s}$ and modeled with a function of acceleration such that:
$$a = - 0.5v$$
(this is derived from a force as a function of velocity)
$$F = 50v = 100\cdot a$$
Then say I wanted to know what v was equal to at the time t = 4 seconds.
I integrated both sides and get:
$$30 - 0.5Δv t = 0.5\Delta x$$
is this correct? I now seem to not have enough variables to solve the equation for v at time $t = 5$. What other equation am I missing? Did I get this equation incorrectly? I can not use UAM equations because this particle is not accelerated at a constant rate, so I must derive kinematic equations from this circumstance?
Any help is appreciated. Thanks.