vt_0

A point moves in the x-y plane according to the equations x=at, y=at-vt^2 Find : (a) the equation of the trajectory, (b) acceleration as s function of t (c) the instant t_0 at which the velocity and acceleration are at pi/4 .

Two waves are smultaneously passing through a string. The equation of the waves are given by y_1=A_1sink(x-vt) and y_2=A_2sink(x=vt+x_0) where the wave number k=6.28 cm^-1 and x_0=o1.50c. The ampitudes of A_1=5.0mm and A_2=4.0mm. find the phase difference between the waves and the amplitude of the resulting wave.

Two waves are simultaneously passing through a string and their equations are : y_1 =A_1 sin k(x - vt), y_2=A_2 sink(x- vt+x_0) . Given amplitudes A_1 =12 mm and A_2 =5 mm, x_0 = 3.5 cm and wave number k = 6.28 cm^( - 1) . The amplitude of resulting wave will be ___________mm.

Two waves are passing through a region in the same direction at the same time . If the equation of these waves are y_(1) = a sin ( 2pi)/(lambda)( v t - x) and y_(2) = b sin ( 2pi)/( lambda) [( vt - x) + x_(0) ] then the amplitude of the resulting wave for x_(0) = (lambda//2) is

The equation y=a sin 2 pi//lamda (vt -x) is expression for :-

If the law of motion in a straight line is s=(1)/(2)vt , then acceleration is

Show that (a)y=(x+vt)^(2),(b)y=(x+t)^(2),(c )y=(x-vt)^(2) , and (d) y=2 sin xcos vt are each a solution of one dimensional wave equation but not (e) y=x^(2)-v^(2)t^(2) and (f) y=sin 2x cos vt.