Motion and Kinematics Key Concepts

Posted on Oct 26, 2024 in Physics

Displacement and Distance

  1. The variation of the position vector that a particle experiences in a time interval is called displacement.
  2. The displacement vector is independent of the path followed by the particle.
  3. The distance traveled by a particle is greater than or equal to the magnitude of the displacement.
  4. The distance traveled is equal to the magnitude of displacement if the path is straight with no change in direction.

Velocity and Speed

  1. If a particle starts at point P and returns to P after a time Δt, the average velocity (vm) is zero.
  2. The instantaneous velocity vector is tangent to the path.
  3. The instantaneous speed is equal to the magnitude of the velocity vector.
  4. If a particle moves with constant velocity (v), its acceleration is 0.

Acceleration

  1. If a particle changes the magnitude of its velocity, tangential acceleration is generated. If it only changes direction, centripetal acceleration is generated.
  2. Curvilinear motion is always accelerated due to centripetal acceleration, as velocity changes direction.

Free Fall and Vertical Motion

  1. When an object falls freely from rest, the acceleration at the end of the sixth second is -9.8 m/s2.
  2. When an object is thrown vertically upwards, the speed decreases by 9.8 m/s2 every second while ascending.

Linear Motion

  1. In uniform linear motion, speed is constant and acceleration is zero.
  2. If a particle moves along a straight path, the normal acceleration is zero since velocity doesn’t change direction.
  3. For a particle moving on a straight line:
    • In the position vs. time graph, the tangent represents instantaneous speed.
    • In the velocity vs. time graph, the tangent represents acceleration, and the area under the curve represents displacement (algebraic sum) or distance (sum of absolute values).
    • If the velocity vs. time graph changes sign, the particle changes its direction of motion.
  4. If speed changes by equal values in equal time intervals, the motion is uniformly accelerated.

Parabolic Motion

  1. Parabolic motion is curvilinear with constant acceleration.
  2. In parabolic motion, the horizontal velocity component is constant. At maximum height, the vertical velocity is zero.
  3. When launching a projectile, speed and gravity form a right angle at maximum height and an acute angle while descending.
  4. Projectile motion is composed of uniform rectilinear motion along the x-axis and uniformly accelerated rectilinear motion along the y-axis, with total acceleration equal to gravity.
  5. In projectile motion, the speed is the same at the same height, ascending or descending.
  6. Maximum range is achieved at a launch angle of 45°.
  7. Complementary launch angles result in equal ranges.

Circular Motion

  1. If a particle travels equal arcs in equal times, the motion is uniform circular.
  2. In uniform circular motion, velocity is tangent to the trajectory and perpendicular to total acceleration, which is equal to centripetal acceleration.
  3. In non-uniform circular motion, angular acceleration is constant, so tangential acceleration is constant, and the magnitude of velocity varies with time.
  4. In non-uniform circular motion, the normal acceleration is greater at larger radii.
  5. If the angle between total acceleration and velocity is acute, the motion is accelerated.

True or False

  1. An object in free fall increases its speed by 0.9 m/s each second. False (9.8 m/s)
  2. Displacement always equals distance in straight-line motion. False
  3. Average velocity is always tangent to the trajectory. False
  4. Instantaneous velocity is always tangent to the path. True
  5. Distance is greater than displacement magnitude in curved paths. True
  6. Average speed equals velocity magnitude in curved paths. False
  7. Curvilinear motion is accelerated. True
  8. Constant speed in curved paths means zero total acceleration. False
  9. If velocity varies only in magnitude, total acceleration is tangential. True
  10. If speed and acceleration are at a 45° angle, normal and tangential acceleration magnitudes are equal. True
  11. Instantaneous displacement indicates instantaneous velocity direction. True
  12. Tangential acceleration is constant and non-zero in uniform rectilinear motion. False
  13. Total acceleration is constant in uniformly varied rectilinear motion. True
  14. A horizontal position vs. time graph means zero velocity. True