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This model applies for a point particle subject to a constant acceleration that is either parallel to or antiparallel to the particle's initial velocity. |
It is a subclass of the
One-Dimensional Motion (General) model defined by the constraint da/dt = 0.
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h4. System Schema
Internal Constituents: None. Object must be treated as a point particle.
External Agents: Some constant external influence must be present which produces the acceleration.
h4. Descriptors
Object Variables: None.
State Variables: Time (_t_), position (_x_) , and velocity (_v_) are possible state variables. Note that in some cases only two of the three possible state variables will be needed.
Interaction Variables: Acceleration (_a_).
h4. Laws of Interaction
Acceleration must be a constant.
h4. Laws of Change
{latex}$v_{\rm f} - v_{\rm i} = a (t_{\rm f} - t_{\rm i})${latex}
{latex} $ x_{\rm f} = x_{\rm i} + \frac{1}{2}(v_{\rm f} + v_{\rm i})(t_{\rm f} - t_{\rm i}) $${latex}
{latex}$ x_{\rm f} = x_{\rm i} + v_{\rm i} (t_{\rm f} - t_{\rm i}) \+ \frac{1}{2} a (t_{\rm f}-t_{\rm i})^{2} ${latex}
{latex}\(v_{\rm f}^{2} = v_{\rm i}^{2} + 2 a (x_{\rm f} - x_{\rm i})\){latex}
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