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.

  1. 👍
  2. 👎
  3. 👁
  1. v = Vi + a t = 0 + a t
    = a t = k/s
    so
    t = k/(a s)

    s = 0 + . 5 a t^2
    = .5 a t^2

    s = .5 a k^2/(a^2 s^2)
    s^3 a = .5 k^2
    a = .5 k^2/s^3

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A ball is thrown straight down from the top of a 445-foot building with an initial velocity of -24 feet per second. Use the position function below for free-falling objects. s(t) = -16t2 + v0t + s0 What is its velocity after 2

  2. Physics

    When is the average velocity of an object equal to the instantaneous velocity? a) always b)never c) only when velocity is constant d)only when velocity is increasing at a constant rate c) would be the answer since you could cross

  3. PHYSICS

    The only force acting on a 2.3 kg body as it moves along the positive x axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s. At what positive value of x will the body have a

  4. 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

  1. physics

    A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the body has a constant speed of 24 meters per second. At t = 1 second, the body is given a constant acceleration of 6

  2. Physics

    At about 51.2 meters/sec, a falling parachuter (before the parachute opens) no longer accelerates. Air friction opposes acceleration. Although the effect of air friction begins gradually, imagine that the parachuter is free

  3. Terminal Velocity

    How can u determine that a falling object has reached terminal velocity from a velocity time graph of its motion? u can determine if a falling object has reached terminal velocity from a velocity-time graph of its motion by its

  4. physics

    Which one of the following situations is not possible? A body travels with a constant acceleration and a time-varying velocity. A body travels with a northward velocity and a northward acceleration. A body travels with a northward

  1. physics

    A 2 kg body and 3 kg body are moving along x-axis .At a particular instant ,the 2 kg body has a velocity of 3 m per sec and the 3 kg body has the velocity of 2 m per sec . The velocity of the center of mass at that instant is.

  2. 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

  3. physics

    1.A body with an initial velocity of 18km/hr accelerates uniformly at the rateof 9cm/sec2over a distance of 200m.Calculate, a)the acceleration in m/sec2 b)its final velocity in m/s 2.The distance travelled by a body moving with

  4. Science

    A falling object is said to be at terminal velocity when the force of gravity pushing it down is exactly counterbalanced by the force of air resistance (a special case of friction) pushing up on it. Given that the net force on an

You can view more similar questions or ask a new question.