Linear Motion

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	\(\large{ sec }\)	\(\large{ s }\)