# Linear Motion

on . Posted in Classical Mechanics 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 $$\large{ sec }$$ $$\large{ s }$$ Tags: Motion Equations