Acceleration Linear Motion Formula |
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\( \overrightarrow{a} \;=\; \dfrac{ \Delta v }{ \Delta t }\) (Acceleration Linear Motion) \( \Delta v \;=\; \overrightarrow{a} \cdot \Delta t \) \( \Delta t \;=\; \dfrac{ \Delta v }{ \overrightarrow{a} }\) |
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| Symbol | English | Metric |
| \( \overrightarrow{a} \) = Linear Acceleration | \(ft\;/\;sec^2\) | \(m\;/\;s^2\) |
| \( \Delta v \) = Velocity Differential | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( \Delta t \) = Time Differential | \( sec \) | \( s \) |
Linear motion, also called rectilinear motion, refers to the motion of an object in a straight line with a constant velocity or changing velocity. In other words, the object moves in a single direction without any rotation or angular movement. Examples of linear motion include a train moving along a straight track, a car moving in a straight line on a highway, or a ball thrown in a straight line. Linear motion can be described mathematically using equations of motion, which relate the displacement, velocity, and acceleration of the object.
Displacement Linear Motion Formula |
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\( \overrightarrow{d} \;=\; v_i \cdot t + \dfrac{1}{2} \: a\cdot t^2 \) (Displacement Linear Motion) \( v_i \;=\; \dfrac{ \overrightarrow{d} }{ t } - \dfrac{ 1 }{ 2 } \cdot a \cdot t \) \( t \;=\; \sqrt{ \dfrac{ 2 \cdot \left( \overrightarrow{d} - v_i \cdot t \right) }{ a } }\) \( a \;=\; \dfrac{ 2 \cdot \left( \overrightarrow{d} - v_i \cdot t \right) }{ t^2 }\) |
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| Symbol | English | Metric |
| \( \overrightarrow{d} \) = Linear Displacement | \( ft \) | \(m \) |
| \( v_i \) = Initial Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( t \) = Time | \( sec \) | \( s \) |
| \( a \) = Acceleration | \(ft\;/\;sec^2\) | \(m\;/\;s^2\) |
Velocity Linear Motion Formula |
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\( \overrightarrow{v_f} \;=\; v_i + a \cdot t \) (Velocity Linear Motion) \( v_i \;=\; \overrightarrow{v_f} - a \cdot t \) \( a \;=\; \dfrac{ \overrightarrow{v_f} - v_i }{ t }\) \( t \;=\; \dfrac{ \overrightarrow{v_f} - v_i }{ a }\) |
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| Symbol | English | Metric |
| \( \overrightarrow{v_f} \) = Linear Final Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( v_i \) = Initial Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( a \) = Acceleration | \(ft\;/\;sec^2\) | \(m\;/\;s^2\) |
| \( t \) = Time | \( sec \) | \( s \) |