calculus
posted by theophilus .
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.

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
Respond to this Question
Similar Questions

Chels
What can you say about the motion of a body if its veloctiytime graph is a straight line inclined with the time axis? 
calc
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 … 
physics
The only force acting on a 3.0 kg body as it moves along the positive x axis has an x component Fx = 9x N, where x is in meters. The velocity of the body at x = 2.3 m is 9.7 m/s. (a) What is the velocity of the body at x = 4.4 m? 
physics
Which one of the following situations is not possible? 
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 … 
Physics
The only force acting on a 4.7 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 = 2.4 m is 11 m/s. (a) What is the velocity of the body at x = 4.9 m? 
physics
A 2 kg body and 3 kg body are moving along xaxis .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. 
Physics
A body of mass m falls from rest through the air. A drag force D = bv^2 opposes the the motion of the body. The acceleration due to gravity is g. A) What is the initial downward acceleration of the body? 
maths /science
A body calling from rest has a velocity of 25m/s at given instant. Calculate 1 the distance the body has fallen 2 the time taken 
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 …