# Linear Motion

on . Posted in Classical Mechanics

Linear motion is a one direction motion on a one dimensional plane using acceleration, displacement, and velocity.

## Linear motion formula

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

## Linear motion formula

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

## Linear motion formula

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

## Linear motion formula

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

Tags: Motion Equations