acceleraion of certain particle is described by a = 16-4v where v is velocity, if when t =0 v is equal to 5 determine the standart equation of v by integrating a
the books shows answer like this
a=dv/dt
16-4v=dv/dt
4(4-v)=dv/dt
-4dt=dv/(v-4) <- integrating both
-4t + C = ln v-4 then determine C by given condition
(t=0 v=5)
C = ln 1 = 0
then v = 4 + e^-4t is the general equation ###book ans###
and my attempt is not simplify the 16-4v to 4(4-v)
but just leave it as 16-4v but it don't give same result
here my attempt
a=dv/dt
16-4v=dv/dt
-dt=dt/(4v-16) then integrating both side
-t + C= ln (4v -16) determine value of C
(when t=0 v=5)
C = ln 4 then back to
-t + ln 4 = ln (4v - 16) or i can write it as
-t = ln(4v - 16) - ln 4 and by logaritm properties is turned to
-t = ln ((4v-16)/4)
4e^-t = 4v -16 simplyfied
4 + e^-t = v ###mine###
There is significant difference between both result, so i hope anyone can show me where did i go wrong
the books shows answer like this
a=dv/dt
16-4v=dv/dt
4(4-v)=dv/dt
-4dt=dv/(v-4) <- integrating both
-4t + C = ln v-4 then determine C by given condition
(t=0 v=5)
C = ln 1 = 0
then v = 4 + e^-4t is the general equation ###book ans###
and my attempt is not simplify the 16-4v to 4(4-v)
but just leave it as 16-4v but it don't give same result
here my attempt
a=dv/dt
16-4v=dv/dt
-dt=dt/(4v-16) then integrating both side
-t + C= ln (4v -16) determine value of C
(when t=0 v=5)
C = ln 4 then back to
-t + ln 4 = ln (4v - 16) or i can write it as
-t = ln(4v - 16) - ln 4 and by logaritm properties is turned to
-t = ln ((4v-16)/4)
4e^-t = 4v -16 simplyfied
4 + e^-t = v ###mine###
There is significant difference between both result, so i hope anyone can show me where did i go wrong