(Solved): Problem 2 [2 points] A particle of mass \( m \) moving through a fluid is subjected to a viscous r ...

Problem 2 [2 points] A particle of mass \( m \) moving through a fluid is subjected to a viscous resistance \( R \), which is a function of the velocity \( v \). The relationship between \( R, v \), and time \( t \) is \[ t=\int_{v\left(t_{0}\right)}^{v(t)} \frac{m}{R(u)} d u . \] Assume \( R(v)=-v \sqrt{v} \) for a particular fluid. If \( m=10 \mathrm{~kg} \) and \( v(0)=10 \mathrm{~m} / \mathrm{s} \), approximate the time for the particle to slow down to \( v=5 \mathrm{~m} / \mathrm{s} \).