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.
Acceleration Linear Motion Formula |
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\( \overrightarrow{a} \;=\; \Delta v \;/\; \Delta t \) (Acceleration Linear Motion) \( \Delta v \;=\; \overrightarrow{a} \; \Delta t \) \( \Delta t \;=\; \Delta v \;/\; \overrightarrow{a} \) |
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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 | \( sec \) | \( s \) |
Displacement Linear Motion Formula |
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\( \overrightarrow{d} \;=\; v_i \; t + \frac{1}{2} a\;t^2 \) (Displacement Linear Motion) \( v_i \;=\; ( \overrightarrow{d} \;/\; t ) - \frac{ 1 }{ 2 } \; a \; t \) \( t \;=\; \sqrt{ 2 \; \left( \overrightarrow{d} - v_i \; t \right) \;/\; a } \) \( a \;=\; 2 \; \left( \overrightarrow{d} - v_i \; t \right) \;/\; t^2 \) |
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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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\( \overrightarrow{v_f} \;=\; v_i + a \; t \) (Velocity Linear Motion) \( v_i \;=\; \overrightarrow{v_f} - a \; t \) \( a \;=\; \overrightarrow{v_f} - v_i \;/\; t \) \( t \;=\; \overrightarrow{v_f} - v_i \;/\; a \) |
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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 | \( sec \) | \( s \) |
