(adsbygoogle = window.adsbygoogle || []).push({}); 1. An object of mass, M, is projected into the air with an initial vertical component of velocity, Vo. If the air resistance is proportional to the instantaneous velocity, with the constant of proportionality being, K, derive the equations for the displacement, velocity and acceleration as functions of time.

appologies for the way this is wrote if anyone has a better way of notating this it would be much appreciated.

my work

m dv/dt=(-mg-kv)

so first I got my V's on one side and my T's on the other

mdv/(mg+kv)=-dtthen added the integral sign to this equation and integrated it too get

m/k ln(mg+kv)=-t+c

next I tidied it up

mg+kv=e^-((k/m)*t)+cthat goop in the middle is meant to be exp to the power of whats in the brackets

mg+kv=ce^-((k/m)*t)movin the c for more tidiness

now I tried to get V on its own

V=ce^-((k/m)*t)-mg/k

sub in t=0 and V=Vo

Vo=C-mg/ktherfore c is

C=Vo + mg/k

subbing back into my previous I got

v=(Vo + mg/k)e^-((k/m)*t)-mg/kthat is my velocity part right

thats pretty much it for me any help would be appreciated for displacement and acceleration[/b]

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# Deriving displacement, velocity and acceleration projecticle motion

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