the acceleration of a certain marble is given by,a=-3(velocity squared)if the marble enters the fluid with a speed of 1.5m/s , how long will it take before marble's speed is reduced to half of its initial value?

Dear student,

a=-3v2

dv/dt=-3v2

dv/v2=-3dt

-1/v=-3t

So u get a relation between velocity and time..

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

a = dv/dt

a = -3v²            (given)

dv/dt = -3v²

dv/v² = -3dt

-1/v = -3t + c        .............1

at t=0 , v = 1.5

c = -2/3

now eq 1 becomes

-1/v = -3t + -2/3           ................2

finally velocity becomes half of original= v = 1.5/2

after putting this in eq 2 we get

t = 2/9 sec

t =