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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.
Prerequisite Vocabulary
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- acceleration (one-dimensional)
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Model Specification borderStyle solid Wiki Markup 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}