An equation of motion when a particle moves in a resting medium is given by dv/dt=−(kv+bt) where k and b are constants. Given that v=u when t=0, show that v(t)=b/k^2−b/kt+(u−b/k^2)e^(−kt)

hikstac0 2022-09-28 Answered
An equation of motion when a particle moves in a resting medium is given by
d v d t = ( k v + b t )
where k and b are constants. Given that v=u when t=0, show that
v ( t ) = b k 2 b k t + ( u b k 2 ) e k t
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Abigayle Lynn
Answered 2022-09-29 Author has 12 answers
v ( t ) = b t k v ( t )
d v ( t ) d t = b t k v ( t )
d v ( t ) d t + k v ( t ) = b t
Let μ ( t ) = e k   d t = e k t

e k t d v ( t ) d t + ( e k t k ) v ( t ) = e k t b t
d d t ( e k t v ( t ) ) = e k t b t
d d t ( e k t v ( t ) )   d t = e k t b t   d t
e k t v ( t ) = b e k t ( k t 1 ) k 2 + C
v ( t ) = b t k b k 2 + C e k t
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more