Question

A particle starts with velocity v0​ at at time t=0 and is decelerated at a rate proportional to the square root of its speed  at time t with constant of proportionality α.The total time for which it will move before coming to rest is-
I will mark Correct answer with explaination as brainliest

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Answer 1

Answer: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 }

i am not sure about this