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Kinematics in One Dimension - Coggle Diagram
Kinematics in One Dimension
Referance Frame and Displacement
Displacement is how far the object is from its starting point, regardless of how it got there.
Distance traveled is measured along the actual path.
The displacement is written:
If direction is right then the value is positive
If direction is left then the value is negative
Acceleration
Acceleration is the rate of change of velocity.
Average Velocity
Instantaneous Velocity
The instantaneous velocity is the average velocity in the limit as the time interval becomes infinitesimally short.
The instantaneous speed always equals the magnitude of the instantaneous velocity; it only equals the average velocity if the velocity is constant.
On a graph of a particle’s position vs. time, the instantaneous velocity is the tangent to the curve at any point.
Motion in Constant Acceleration
Free Falling Object
Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity.
In the absence of air resistance, all objects fall with the same acceleration, although this may be tricky to tell by testing in an environment where there is air resistance.
Graphical Analysis and Numerical Integration
The total displacement of an object can be described as the area under the v-t curve:
Similarly, the velocity may be written as the area under the a-t curve.
However, if the velocity or acceleration is not integrable, or is known only graphically, numerical integration may be used instead.
Integral Calculus
Deriving the kinematic equations through integration:
For constant acceleration,
