KINEMATICS DEFINITIONS

Trajectory

It is the shape of the path followed by a moving object. It is also the graph obtained by joining all the points through which the object passes.

Distance or Path Length (d)

It is the length of the trajectory.

Dimension: d ⇾ [ L ]

Position Vector (r)

Also called the radius vector, it is the vector that goes from the coordinate origin to any point in the Cartesian plane or three-dimensional space.

Dimension: r ⇾ [ L ]

Displacement (Δr)

It is the vector that goes from an initial point to a final point. It does not depend on where the coordinate origin is placed.

Dimension: Δr ⇾ [ L ]

By deducing the vector equation of vector addition using the polygon method, we obtain:

displacement position formula

Therefore, mathematically:

initial final displacement formula

Relative Position Vector (rA/B)

We use the relative position vector when we want to find the position of one point with respect to another point.

Average Velocity

It is the relationship between the displacement made by a moving object and the time interval used during that displacement.

Dimension: Vm ⇾ [ LT-1 ]

Instantaneous Velocity

It is the limit of average velocity when the time interval approaches zero.

Instantaneous velocity is always tangent to the trajectory.

Average Speed

It is the relationship between the distance traveled and the time used.

Dimension: Vm ⇾ [ LT-1 ]

Instantaneous Speed (Vinst)

It is the magnitude of instantaneous velocity.

Important Notes

  • Velocity is a vector quantity, while speed is a scalar quantity.
  • When we simply say velocity, we refer to instantaneous velocity.
  • If velocity is constant, average and instantaneous velocity are the same.
  • If speed is constant, average and instantaneous speed are the same.
  • Average speed is not equal to the magnitude of average velocity unless the motion is rectilinear without changes in direction.

Average Acceleration

It is the relationship between the variation in velocity and the time interval used.

Dimension: am ⇾ [ LT-2 ]

Instantaneous Acceleration

It is the limit of average acceleration when the time interval approaches zero.

Acceleration can be decomposed into tangential acceleration and centripetal acceleration.

Tangential Acceleration

This acceleration changes the magnitude of velocity. If motion is rectilinear, it may only have tangential acceleration.

Centripetal or Normal Acceleration

This acceleration changes only the direction of velocity, not its magnitude. Every curvilinear motion necessarily has centripetal acceleration.

Important Notes

  • Acceleration is a vector quantity.
  • When we simply say acceleration, we refer to instantaneous acceleration.
  • If acceleration is constant, average and instantaneous acceleration are the same.

Kinematics Problems

1.- A particle is located at point A (-200,0) m, and after traveling a semicircle in 10 seconds, it reaches point B (100,400) m. Determine:

a) The average velocity from A to B.

b) The average velocity from A to a point C located halfway along the trajectory.

c) The instantaneous velocity at point A, assuming constant speed.

d) The instantaneous velocity at point C, assuming constant speed.

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