Diff Eq

posted by .

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, there will always be a decelerating force, due to friction,
air resistance, or viscous drag. This drag force increases in magnitude as the speed increases, and
as long as the speed is not too large, it is reasonable to assume direct proportionality. That is, in
addition to the constant acceleration a, the body experiences a deceleration proportional to velocity,
say, v, where  is a positive constant of proportionality (the drag coecient). Since acceleration
equals rate of change of velocity, it follows that v_ = a 􀀀 v, or equivalently,
v_ + v = a:
(a) Given the body's initial velocity, v(0) = v0, derive a formula for the body's velocity, v = v(t),
as a function of time t. Qualitatively sketch the graph of v = v(t) in each of the relevant cases
(v0 < a
, v0 = a
, v0 > a
) and give a physical interpretation of the results. What is the physical
signi cance of the quantity a
? What is the physical dimension of the drag coecient , and what
is the physical signi cance of its reciprocal, 1
(b) Given the body's initial velocity, v(0) = v0, and initial position, x(0) = x0, derive a formula for
the body's position, x = x(t), as a function of time t. (Position is measured, relative to a reference
point x = 0, along the line of motion, in the same direction as v.) Hint: Use the formula for v
obtained in (a), along with the fact that velocity equals rate of change of position (that is, x_ = v)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. science

    Couple of questions. Why does the earth keep moving?
  2. physics # 1

    1. If a particle moves in a plane so that its position is described by the function x = Acosùt, and y = Asinùt, it is a.) moving with varying speed along a circle b.) moving with constant speed along a circle c.) moving with constant …
  3. Chels

    What can you say about the motion of a body if its veloctiy-time graph is a straight line inclined with the time axis?
  4. AP Physics

    While two forces act on it, a particle is to move at the constant velocity v = (3 m/s) i - (4 m/s) j. One of the forces is F1 = (2 N) i + (- 6 N) j. What is the other force?
  5. Physics

    (10 points) 3. Use your data from Part 3 and Newton’s laws to explain why the force meter measures a force if the cart is moving at a constant velocity. The forces acting on the cart are the applied force (FA), the force of friction …
  6. Physics

    A skier of mass 66 kg skis straight down a 11° slope at constant velocity. Draw a free-body diagram of the skier with the various external forces acting on her. Include the force of air resistance, which is directed opposite the velocity. …

    1.Two trolleys X and Y with momenta 20 Ns and 12 Ns respectively travel along a straight line in opposite directions before collision. After collision the directions of motion of both trolleys are reversed and the magnitude of the …
  8. physics

    A body starts with an initial velocity of 10m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50 m/s the acceleration is reversed in direction without changing magnitude. Find …
  9. shahabdulatif science

    the velocity of the body moving in a straight line with a constant acceleration, is 10 m/s at a certain instant 't' . after 5 second the velocity become 20 m/s, the velocity 3 second before 't' was?
  10. Physics y.s.n.

    A body start with an initial velocity of 10metre per second move along the straight line with constant acceleration and the velocity of the body is 50 metre per second the acceleration is reversein the direction find the velocity of …

More Similar Questions