Question

A particle retards from a velocity v0 while moving in a straight line. If magnitude of deceleration is directly proportional to the square root of the speed of the particle, find average velocity for the total time of it's motion.

Answer 1

let a is the magnitude of deceleration .
and v is the speed of particle .

a/c to question,
a =K√v { where K is the constant

dv/dt =K√v

dv/√v = K.dt

integrate both sides ,
[ 2√v ] = K [ t ] put the limit

2[ √v - √vo ] = Kt

2√v = kt + 2√vo

√v ={ kt + 2√vo }/2

v = { K/2.t + √vo }²