the velocity (v) of a body moving along positive x-direction varies with displacement (x) as v=krootx, where k is a - Physics - Kinematics

Question

the velocity (v) of a body moving along positive x-direction varies
with displacement (x) as v=krootx, where k is a constant Determine
how (v) varies with time (t) Also , find the variation of x and t

Vijay Shankar Yadav · Accepted Answer

Dear Student,
here given v=kx-----1or v2=k2xdifferentiate with respect to  x we get 2vdvdx=k2or2vdv=k2dxdtdt=k2vdt∫0v2dv=∫0tk2dtv=k2t/2from equation 1 dxdt=kx∫0xdxx=∫0tkdt-2x=ktx=k2t24
Regard

the velocity (v) of a body moving along positive x-direction varies with displacement (x) as v=krootx, where k is a constant . Determine how (v) varies with time (t) . Also , find the variation of x and t.