# 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

$$\overrightarrow{a} = \Delta v \;/\; \Delta t$$     (Acceleration Linear Motion)

$$\Delta v = \overrightarrow{a} \; \Delta t$$

$$\Delta t = \Delta v \;/\; \overrightarrow{a}$$

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

$$\overrightarrow{d} = v_i \; t + \frac{1}{2} a\;t^2$$     (Displacement Linear Motion)

$$v_i = ( \overrightarrow{d} \;/\; t ) - \frac{ 1 }{ 2 } \; a \; t$$

$$t = \sqrt{ 2 \; \left( \overrightarrow{d} - v_i \; t \right) \;/\; a }$$

$$a = 2 \; \left( \overrightarrow{d} - v_i \; t \right) \;/\; t^2$$

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

$$\overrightarrow{v_f} = v_i + a \; t$$     (Velocity Linear Motion)

$$v_i = \overrightarrow{v_f} - a \; t$$

$$a = \overrightarrow{v_f} - v_i \;/\; t$$

$$t = \overrightarrow{v_f} - v_i \;/\; a$$

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 $$sec$$ $$s$$

Tags: Motion