Fundamental Kinematics Definitions

Posted on May 20, 2025 in Geology

Key Concepts in Kinematics

  1. The variation of the position vector of a particle that it experiences in a time interval is called displacement.
  2. The displacement vector is independent of the trajectory that the particle follows in its motion.
  3. The distance traveled by a particle is greater than or equal to the magnitude of the displacement vector experienced by the particle when moving from one position to another.
  4. The distance traveled by a particle is equal to the magnitude of the displacement vector, provided the trajectory is rectilinear and there is no change in the direction of motion.
  5. If a particle starts its motion at point p, and after a certain time, it returns to the same position, the average velocity vector (vm) is zero.
  6. The velocity vector is in the tangential direction at the point of analysis on the trajectory.
  7. When an object falls freely from an initial position, its acceleration is -9.8 m/s².
  8. Instantaneous speed is the magnitude of the velocity vector.
  9. If a particle moves with constant velocity (v), its acceleration is equal to 0.
  10. If a particle changes the magnitude of its velocity, tangential acceleration is generated, and if it only changes direction, centripetal acceleration is generated.
  11. Curvilinear motion is always accelerated because there is centripetal acceleration, since the velocity changes direction.
  12. When an object is thrown vertically upwards, its speed decreases by 9.8 m/s each second while ascending.
  13. In uniform rectilinear motion, the velocity is constant and the acceleration is zero.
  14. If a particle moves along a rectilinear path, its normal acceleration is zero because the direction of velocity does not change.
  15. When a particle moves along a rectilinear trajectory:
    1. In the graph of position versus time, the value of the tangent at each point represents the instantaneous velocity.
    2. In the graph of velocity versus time, the value of the tangent at each point represents the acceleration; the area under the curve represents the magnitude of the displacement if the algebraic sum of the areas is used, or the distance traveled if the sum of the absolute values of the areas is considered over a given time interval.
    3. In the graph of velocity versus time, if it changes sign at some time (t), it means that at that instant the particle changes or reverses its direction of motion.
  16. In rectilinear motion, if the magnitude of the velocity changes by equal values in equal time intervals, the motion is uniformly accelerated.
  17. Parabolic motion is curvilinear motion with constant acceleration.
  18. In parabolic motion, at the point of maximum height, the velocity vector is perpendicular to the total acceleration vector (gravity). At this instant, the total acceleration is equal to the centripetal acceleration.
  19. When launching a missile, while ascending, the velocity vector and the gravity vector form an angle. At the point of maximum height, they are perpendicular. While descending, they form an acute angle.
  20. Projectile motion is considered a composite motion, formed by uniform rectilinear motion in the horizontal direction (e.g., x-axis) and uniformly accelerated motion in the vertical direction (e.g., y-axis), where the total acceleration is due to gravity.
  21. In a missile launch, when it passes through the same height while ascending and descending, the magnitude of the velocity is equal.
  22. The optimum launch angle (elevation) for maximum range of a projectile is 45°.
  23. For launch angles (elevation) that are complementary, the ranges are equal.
  24. If a particle in circular motion covers equal arcs in equal times, the motion is uniform circular motion.