The velocity in `ft//sec` of a falling object is modeled by `r(t)=-sqrt(32/k) (1-e^(-2tsqrt32k))/(1+e^(-2tsqrt23k))` where k is a constant that depends upon the size and shape of the object and the density of the air. Find the limiting velocity of the object , that is find `lim_(l to infty) r(t)`.

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

The velocity v, of a parachute falling vertically satisfies the equation v(dv)/(dx)=g(1-v^(2)/(k^(2))) , where g and k are constants. If v and x are both initially zero, find v in terms of x.

Let z=t^2-1+sqrt(t^4-t^2),w h e r et in R is a parameter. Find the locus of z depending upon t , and draw the lous of z in the Argand plane.

The position of a particle is given by r=2.00t hati-1.00t^(2)hatj+3.00hatk where t is in seconds and the coefficients have the proper unit for r to be in metres. Find the velocity and acceleration of a particle then what is the magnitude and direction of velocity of the particle at t = 2 s?

If the position vector of a particle is given by vec r= 5t^(2)hat i +7t hat j +4 hat k , then its velocity lies in:

Draw the graph of f(x)=log_(e)(sqrt(1-x^(2))) .Find the range of the function .Also find the values of k if (k) has two distinct real roots.

The electric current in a discharging R-C circuit is given by i=i_0e^(-t/(RC)) where i_0 R and C are constant parameters and t is time. Let i_0=2.00A , R=6.00xx10^5 ohm and C=0.500 muF . a. Find the current at t=0.3 s. b. Find the rate of change of current at t=0.3 s. Find approximately the current at t=0.31 s.