# DISPLACEMENT, VELOCITY AND ACCELERATION CALCULATOR

Displacement, velocity and acceleration calculator calculates displacement, distance, initial velocity, final velocity, average velocity, average speed, elapsed time and acceleration parameters of an object with uniform acceleration. Kinematic equations, which are used for each calculation case, are given below the calculator.

## Displacement, Velocity and Acceleration Formulas

If initial velocity, final velocity and elapsed time parameters are known;

$$a={ { (V }_{ f }-{ V }_{ 0 }) }/{ t }$$
$$\Delta x={ V }_{ 0 }t+0.5a{ t }^{ 2 }$$

If initial velocity, final velocity and acceleration parameters are known;

$$t={ { (V }_{ f }-{ V }_{ 0 }) }/{ a }$$
$$\Delta x={ V }_{ 0 }t+0.5a{ t }^{ 2 }$$

If final velocity, acceleration and elapsed time parameters are known;

$${ V }_{ 0 }={ V }_{ f }-at$$
$$\Delta x={ V }_{ 0 }t+0.5a{ t }^{ 2 }$$

If initial velocity, acceleration and elapsed time parameters are known;

$${ V }_{ f }={ V }_{ 0 }+at$$
$$\Delta x={ V }_{ 0 }t+0.5a{ t }^{ 2 }$$

If initial velocity, displacement and elapsed time parameters are known;

$$a={ (\Delta x-{ V }_{ 0 }t) }/{ (0.5{ t }^{ 2 }) }$$
$${ V }_{ f }={ V }_{ 0 }+at$$

If final velocity, displacement and elapsed time parameters are known;

$$a={ (\Delta x-{ V }_{ f }t) }/{ (-0.5{ t }^{ 2 }) }$$
$${ V }_{ 0 }={ V }_{ f }-at$$

If displacement, initial velocity and acceleration parameters are known;

$${ V }_{ f }=\sqrt { { V }_{ 0 }^{ 2 }+2a\Delta x }$$
$$t={ { (V }_{ f }-{ V }_{ 0 }) }/{ a }$$

If displacement, final velocity and acceleration parameters are known;

$${ V }_{ 0 }=\sqrt { { V }_{ f }^{ 2 }-2a\Delta x }$$
$$t={ { (V }_{ f }-{ V }_{ 0 }) }/{ a }$$

General formulas for each case;

$${ V }_{ avg }={ \Delta x }/{ t }$$
$$Distance=\int _{ { t }_{ 0 } }^{ { t }_{ f } }{ \left| v(t) \right| dt }$$
$$Average Speed =distance/time$$