Kinematic Equations
We now use the defining equations for acceleration and velocity to derive two of our kinematic equations:
υxf = υxi + axt (for constant ax) (3)
and
xf = xi + υxi t+1/2axt2 (for constant ax) (4)
The defining equation for acceleration,
ax =dυx/dt
may be written as dυx = ax dt or, in terms of an integral (or antiderivative), as
3. Summary(Lectures 1 – 3 )
Definitions
When a particle moves along the x axis from some initial position xi to some final position xf , its displacementis
Δx = xf - xi
The average velocityof a particle during some time interval is the displacement Δx divided by the time interval Δt during which that displacement occurs:
υx,avg = Δx/Δt
The average speedof a particle is equal to the ratio of the total distance it travels to the total time interval during which it travels that distance
υavg = d/Δt
The instantaneous velocity of a particle is defined as the limit of the ratio Δx/Δt as Δt approaches zero. By definition, this limit equals the derivative of x with respect to t, or the time rate of change of the position:
The average accelerationof a particle is defined as the ratio of the change in its velocity Δυx divided by the time interval Δt during which that change occurs:
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