Linear Motion

on . Posted in Classical Mechanics

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Linear motion, also known as 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

\(\large{ \overrightarrow{a} =  \frac{ \Delta v }{ \Delta t }  }\) 
Symbol English Metric
\(\large{ \overrightarrow{a} }\) = linear acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)
\(\large{ \Delta v }\) = velocity differential \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ \Delta t }\) = time differential \(\large{ sec }\) \(\large{ s }\)

 

Displacement Linear motion formula

\(\large{ \overrightarrow{d} = v_i \; t + \frac{1}{2} a\;t^2  }\) 
Symbol English Metric
\(\large{ \overrightarrow{d} }\) = linear displacement \(\large{ ft }\)  \(\large{ m }\) 
\(\large{ v_i }\) = initial velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ t }\) = time \(\large{ sec }\) \(\large{ s }\)
\(\large{ a }\) = acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)

 

Velocity Linear motion formula

\(\large{ \overrightarrow{v_f} =  v_i + a\;t  }\) 
Symbol English Metric
\(\large{ \overrightarrow{v_f} }\) = linear final velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ v_i }\) = initial velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ a }\) = acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)
\(\large{ t }\) = time \(\large{ sec }\) \(\large{ s }\)

 

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Tags: Motion Equations