# 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 it starts from rest (v=0 at t=0). [Hint: Change variables by setting u=g-kv.] (b) Determine an expression for the terminal velocity, which is the maximum value the velocity reaches.

1. 👍
2. 👎
3. 👁
1. using their hint, let u = g-kv
du/dt = -k dv/dt

-1/k du/dt = u
du/u = -k dt
log u = -kt
u = e^(-kt)
g-kv = e^(-kt)
v = (g-e^(-kt))/k
= g/k - 1/k e^(-kt)

So, max v is g/k as t->infinity

1. 👍
2. 👎

## Similar Questions

1. ### Science

Which statement explains why astronauts appear to bounce when they are walking on the moon? 1. The force of gravity acting on the astronauts is weaker on the moon than the earth. 2. The force of air resistance acting on the

2. ### calculus help check and help

if an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is v= mg/c(1-e^(-ct/m)) where g is the acceleration due to gravity and c is a positive constant

3. ### physics

A 2.2 kg rock initially at rest loses 412 J of potential energy while falling to the ground. Assume that air resistance is negligible. Calculate the kinetic energy that the rock gains while falling. What is the rock's speed just

4. ### Physics

Consider a coin which is tossed straight up into the air. After it is released it moves upward, reaches its highest point and falls back down again. Air resistance can be neglected. What force acts upon the coin while it moves

1. ### Math

The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2 where g is constant at 10 m/s2 Show, in terms of n, the distance a falling body covers in t = n seconds of movement. Show, in terms

2. ### Physics

If a 3 kg object is falling at terminal velocity, what upward force of air resistance does it experience?

3. ### Physics

A ball of mass 8 kg falls from rest from a height of 100 m. Neglecting air resistance, calculate its total energy after falling a distance of 40 m.

4. ### Science

A 50N object falling in air experiences 30N of air resistance. The amount of net force on the falling object is A 0n B 20n C 50n D 80n

1. ### Physics

An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f = bv. Assume b = 19

2. ### physics

What is the net force acting on a 25-N freely falling object? What is the net force when the object encounters 15N of air resistance? When it falls fast enough to encounter 25N of air resistance?

3. ### Physics

please check: 1. A piece of chalk is dropped by a teacher walking at a speed of 1.5 m/s. From the teacher's perspective, the chalk appears to fall. STRAIGHT DOWN 2. Which is the force of an acceleration? FORCE 3. A free-body

4. ### physics

A skydiver jumps out of a plane. Does the mechanical energy of the jumper change while she is falling? Ignore the effects of air resistance.