Calculus · Calculus — University

Video solutions

• Kinematics with Polynomial Position Functions
  Calculus · Calculus — University

  A particle moves along a straight line with position $s = (10t^2 + 20)$ mm. Find: (a) Displacement from $t = 1$ s to $t = 5$ s (b) Average velocity over that interval (c) Acceleration at $t = 1$ s

• Position, Displacement, and Total Distance Using Derivatives
  Calculus · Calculus — University

  Given the position function $s = 1.5t^3 - 13.5t^2 + 22.5t$ ft, where $t$ is in seconds, find: 1. The position at $t = 6$ s 2. The total distance traveled from $t = 0$ to $t = 6$ s

• Velocity as a Function of Position Under Constant Acceleration
  Calculus · Calculus — University

  A particle travels along a straight line with constant acceleration. Given: when $s = 4$ ft, $v = 3$ ft/s; when $s = 10$ ft, $v = 8$ ft/s. Find $v$ as a function of $s$.

• Kinematics via Differentiation and Integration
  Calculus · Calculus — University

  Given: $v = (6t - 3t^2)$ m/s, $s = 0$ when $t = 0$. Find at $t = 3$ s: 1. **Deceleration (acceleration)** 2. **Position $s$** 3. **Total distance traveled** 4. **Average speed**

• Kinematics with Calculus: Velocity, Acceleration, and Distance
  Calculus · Calculus — University

  A particle moves along a straight line with velocity $v = (12 - 3t^2)$ m/s. At $t = 1$ s, the position is $x = -10$ m (10 m to the left of the origin). Find: 1. The acceleration at $t = 4$ s 2. The displacement from $t =…

• Kinematics: Position Under Constant Acceleration
  Calculus · Calculus — University

  A particle has an initial velocity of $v_0 = +12 \text{ ft/s}$ (to the right), an initial position of $s_0 = 0$, and a constant acceleration of $a = -2 \text{ ft/s}^2$ (to the left). Find the position $s$ of the particle…

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