Principles of Biomechanics - Kinematics
Key Concepts in Kinematics provide a framework for understanding basic kinematic quantities and concepts, including:
Position
Velocity
Acceleration
Calculations related to position and velocity for constant acceleration.
Position: The location of an object relative to a reference point.
Displacement: The change in position.
Distance: The magnitude of the displacement.
Example: If the reference point is at x₀ = 0 m and an object moves to x₀ = 2.0 m, the displacement (∆x) is 2.0 m (movement to the right is considered positive).
All measurements are in units of length (m).
Scalars and Vectors:
Vectors: Quantities that possess both magnitude and direction (e.g., displacement).
Scalars: Quantities that have only magnitude without direction (e.g., distance).
Example of vector addition may involve multiple displacement vectors resulting in a net vector.
Velocity (v):
Defined as the displacement (∆x) divided by the time interval (∆t).
Formula: v = ∆x/∆t
Example: If a teacher walks 2.0 m in 1 second, v = ∆x/∆t = 2.0m/1.0s = 2.0m/s.
Speed: The magnitude of the velocity without considering direction; classified as a scalar.
Units of measurement: meters per second (m/s).
Acceleration (a):
Represents the change in velocity (∆v) divided by the time interval (∆t).
Formula: a = ∆v/∆t
Acceleration is a vector quantity, measured in units of length/(time)² (m/s²).
Change in velocity (∆v) over time can be represented as: ∆v = a∆t.
Constant Acceleration Considerations:
Initial velocity at time t = 0 is (vᵢ), while velocity at time t is (vₜ).
Time change (∆t) is expressed as t - 0 = t.
Change in velocity (∆v) is defined as vₜ - vᵢ.
Average velocity (v_{avg}) can be calculated using:
v_{avg} = (vᵢ + vₜ)/2.
Displacement (d) can be determined through:
d = v_{avg} · t = ((vᵢ + vₜ)/2) · t.
Relationships:
∆v = a∆t.
vₜ = vᵢ + at.
d = vᵢt + (1/2) a t².
Standard Acceleration:
The standard acceleration due to gravity is approximately g = 9.81 m/s².