The solution of `(d v)/(dt)+k/m v=-g` is

Find the particular solution of v(dv)/(dx)=n^(2)x , given v=u when x=a

A object falls from rest through a resistive medium. The equation of its motion is (dv)/(dt) = alpha -beta v. Then

If 1 mol of an electrolyte is dissolved in V cm^(3) of a solution, then molar conductivity of the solution is Lambda_(m) = conductivity of the solution xx V. If the concentration of the solution is (M)/(10), then find the value of V.

The function u=e^xsinx and v=e^xcosx . The value of (d^2v)/(dx^2) is-

The motion of a body is defined by (dv(t))/(dt) = 6-3 v(t) where v (t) is the velocity (in m/s ) of the body at time t (in seconds ). If the body was at rest at t= 0 , find its velocity (in m/s ) when the acceleration is half the initial value.

The mole fraction of a solute in a binary solution is 0.1. At 298 K, molarity of this solution is same as its molality. Density of this solution at 298 K is 2.0 g cm^(-3) . The ratio of molecular weights of the solute and the solvent (M_("solute")//M_("solvent")) is

The reaction -rate of the reaction AB_(3)rarr(1)/(2)A_(2)+(3)/(2)B2 can be expressed by any one of the following equations : (-d[AB_(3)])/(dt)=k_(1)[AB_(3)], (d[A_(2)])/(dt)=k_(2)[AB_(3)] " or, " (d[B_(2)])/(dt)=k_(3)[AB_(3)] The ratio between k_(1) , k_(2)and k_(3) is -

Show that , the solution x = e^(-kt) (a cos nt + b sin nt ), for all a and b , always satisfies the differenital equation (d^(2)x)/(dt^(2)) + 2k (dx)/(dt) + (k^(2) + n^(2)) x = 0

An object moving with a speed of 6.25 "m.s"^(-1) is decelerated at a rate given by: (dv)/(dt) = -2.5 sqrt(v) where v is the instantaneous speed. What would be the time taken by the object to come to rest?