# Kinematics

$${dV \over dt} = {\operatorname{change in volume} \over \operatorname{respect to time}}$$

**position $x$** - distance from origin or fixed point  
**displacement $s$** - change in position from starting point (vector)  
**velocity $v$** - change in position with respect to time  
**acceleration $a$** - change in velocity  
**speed** - magnitude of velocity  

$$v_{\operatorname{avg}}={\Delta x \over \Delta t}={{x_2 - x_1} \over {t_2 - t_1}}$$
$$\operatorname{speed}_{\operatorname{avg}}={\Delta v \over \Delta t}$$

## Constant acceleration

| | no |
| - | -- |
| $v=u+at$ | $s$ |
| $s=ut + {1 \over 2} at^2$ | $v$ |
| $v^2 = u^2 + 2as$ | $t$ |
| $s= {1 \over 2}(u+v)t$ | $a$ |

## Velocity-time graphs

- area = displacement

## Definite integrals

$$\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)$$