Differential Equations Differential Equations · Differential Equations — University

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• Kinematics via Separable ODEs: Position and Acceleration from a Velocity Law
  Differential Equations Differential Equations · Differential Equations — University

  The velocity of a particle traveling along a straight line is $v = v_0 - ks$, where $k$ is a positive constant. If $s = 0$ when $t = 0$, determine the position $s(t)$ and acceleration $a(t)$ of the particle as functions …

• Solving a Separable ODE for Terminal Velocity Kinematics
  Differential Equations Differential Equations · Differential Equations — University

  A particle falls through air with acceleration given by $$a = \frac{g}{v_f^2}\left(v_f^2 - v^2\right)$$ where $g$ is gravitational acceleration and $v_f$ is the terminal velocity. The particle starts from rest. Determine…

• Kinematics with Velocity-Dependent Acceleration
  Differential Equations Differential Equations · Differential Equations — University

  A particle moves along a straight line with acceleration defined as $a = -2v$ m/s², where $v$ is in m/s. Given that $v = 20$ m/s when $s = 0$ m and $t = 0$ s, determine $s(t)$, $v(t)$, and $a(t)$.

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