The (non-constant) acceleration as a function of time, $a(t)$, is defined and known over $[t_0, t_2]$. It is also known that $a(t)$ is integrable. Also, $a(t)=\frac{dv(t)}{dt}$ and $v(t)=\frac{dx(t)}{dt}$, where $v(t)$ is the velocity function and $x(t)$ is the distance function. $t_1$ is a known time within $[t_0, t_2]$. Given $v(t_1)$ and $x(t_1)$, is it possible […]

I ve tried to solve this problem in so many ways but still didn’t manage to do it… What would be the correct way to solve it please? This arm of this mechanism has a length of 0,2m. The piston has an angular velocity of 2000 tours/min clockwise. What would be the velocity of point […]

While reading Chapter 1 of an astrodynamics textbook, I came across the statement: $$\mathbf{v}\cdot \mathbf{{\dot{v}}}=v{\dot{v}}$$ In other words, the dot product of velocity and the time-rate-of-change of velocity is simply equal to the product of the magnitudes of the velocity and acceleration vectors. I think I see how this works mathematically: $$\frac{1}{2}\frac{d}{dt}\left ( \mathbf{v}\cdot \mathbf{v} […]

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