# Constant Acceleration

on . Posted in Classical Mechanics

Constant acceleration, abbreviated as $$a_c$$, of an object is the constant rate in a straight line at which the velocity changes with respect to time.  These formulas can not be used if acceleration is not constant.  The following five formulas are for used for constant acceleration.

## Constant Acceleration formula

$$\large{ v = v_i + a\;t }$$
Symbol English Metric
$$\large{ v }$$ = 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 $$\large{sec}$$ $$\large{s}$$

## Constant Acceleration formula

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

## Constant Acceleration formula

$$\large{ d = v_i \; t + \frac{1}{2} a \;t^2 }$$
Symbol English Metric
$$\large{ d }$$ = 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 $$\large{sec}$$ $$\large{s}$$
$$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

## Constant Acceleration formula

$$\large{ d = v \; t - \frac{1}{2} a \;t^2 }$$
Symbol English Metric
$$\large{ d }$$ = 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 $$\large{sec}$$ $$\large{s}$$
$$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

## Constant Acceleration formula

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