Physics problem

[legendary loser]

Hello

i was unable to do this homework problem. If anyone can help i would appreciate it. Thanks.

The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared, and is given (in SI units) by a = -2.60v2 for v > 0. If the marble enters this fluid with a speed of 1.50 m/s, how long will it take before the marble's speed is reduced to half of its initial value?

[slickpoppa]

By how long, do you mean time or distance?

[Borodog]

a = dv/dt = -2.6(m^-1)v^2

dv/v^2 = -2.6(m^-1)dt

Integrate both sides from v0 to v and from 0 to t:

1/v0 - 1/v = -2.6(m^-1)t

t = .385m[1/v - 1/v0]

v = v0/2

t = 0.385m[2/v0 - 1/v0] = 0.385m/v0 = 0.256 s

[legendary loser]

thanks for your help