Physics Help Forum Dynamics Of Material Point

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 May 31st 2019, 11:22 AM #1 Junior Member   Join Date: May 2019 Posts: 1 Dynamics Of Material Point i attempted to solve it with energy formulas . but couldn't find a proper solution.
 Jun 1st 2019, 04:51 AM #2 Senior Member   Join Date: Aug 2010 Posts: 434 I am not sure why you would attempt "to solve it using energy methods" when you are given forces. If there is no driving force them "force= mass times acceleration" gives $m\frac{dv}{dt}= -m(\alpha v+ \beta v^2)$. The "m"s cancel and we can "separate" the variables v and t as $\frac{dv}{\alpha v+ \beta v^2}= dt$. Integrate both sides. $\int \frac{dv}{\alpha v+ \beta v^2}= \int \frac{dv}{v(\beta v+ \alpha)}$. Use "partial fractions". ("decreased twice" is a very strange phrase. Going from $v_0$ to $\frac{v_0}{2}$ would be "decreased by half".) topsquark likes this.

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