calc
posted by Joe .
Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration:
a=dv/dt=gkv where k is constnat
Derive a formula for the velocity of the body as a function of time assuming it starts from rest (v=0 at t=0)
v=?

Integral of dv/(g  kv) = integral of dt
Integrate both sides, from time from 0 to t; and v from 0 to v, for an equation for t in terms of v. Then invert the equation for v(t) 
It would be great to see how this is done. The prof's way of doing it is way confusing and intricate and I just started learning integrals.

This is why you'd need to do exercises in integration.
To give you a hint,
∫dv/(gkv) = log(gkv)/k
This could be inferred from standard integrals:
∫dx/(a+bx) = (1/b)log(a+bx) 
I agree. I suspect the Prof's method is confusing because you don't understand it....you learn by experience spaced over time. There is no substitute in calculus for hump, grunt, and strain...that is, practice, trial and error.
Respond to this Question
Similar Questions

Physics
Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration. a= dv/dt= gkv, where k is a constant. A) Derive a formula for the velocity of the body as a function of time assuming … 
College Physics
A paratrooper w/ a fully loaded pack has a mass of 120kg. The force due to air resistance on him when falling w/ an unopened parachute has magnitude F(sub)d = bv^2, where b=0.14 N*s/m^2. a) if he is falling w/ an unopened parachute … 
AP Physics
I'm trying to derive the formula v^2 = v0^2 + 2a(xx0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when constant … 
calculus
Suppose that the velocity of a falling body is v = k/s (k a constant) at the instant the body has fallen s meters from its starting point. Find the body's acceleration as a function of s. 
physics
a body is thrown vertically upward return to the earth in 3sec. (a)what was the initial velocity of the body (b)what height did the body reach? 
physics
Consider a body falling through the air. The force due to air resistance is given by, F(air)=CAv^2, where C is the coefficient of air friction, A is the area facing the direction of the motion, and V is the velocity of the object with … 
Diff Eq
Consider a body moving along a straight line, in the presence of an external force providing constant acceleration a. In the absence of other forces, the velocity v of the body would increase without bound if a 6= 0. But in reality, … 
Physics
Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration: a= dv/dt = g  kv, where k is a constant. (a) Derive a formula for the velocity of the body as a function of time assuming … 
Calculus  Falling Body Problem
Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 3000 feet with a … 
Physics
A spherical body of diameter 4cm falls freely through air with the velocity of 0.5m/s. The coefficient of velocity of air is 2*10^5Nm/m^2.find the viscous force acting on the body.