The following are the important kinematics equations list. I will also provide a link to google docs file from where you can download the file as pdf (see at the end of the article).

## Physics - Kinematics Equations

### Average Velocity and speed

\[v_{avg} = \frac{\Delta s} {\Delta t} \\\text{Average Speed} = \frac{\text{Total distance}}{\text{time taken}}

\]

### Instantaneous velocity and speed

$v = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta s} \over {\Delta t}} = {{ds} \over {dt}}$Instantaneous speed or speed is the magnitude of the instantaneous velocity

here $s$ is the displacement of the object and has only one component(out of x, y and z) for motion along straight line and has two components for motion in a plane.

### Average acceleration

$${a_{avg}} = {{\Delta v} \over {\Delta t}}$### Instantaneous acceleration

$$a = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta v} \over {\Delta t}} = {{dv} \over {dt}}$$### Equations of motion (constant acceleration)

### Free fall acceleration

$$v = {v_0} + gt$$ $$x = {x_0} + {v_0} + {1 \over 2}g{t^2}$$ $${v^2} = {v_0}^2 + 2g(x - {x_0})$$### Projectiles

**Horizontal distance**$$x = {v_x}t$$

**Horizontal velocity**$${v_x} = {v_{x0}}$$

**Vertical distance**$$y = {v_{yo}}t - {1 \over 2}g{t^2}$$

**Vertical velocity**$${v_y} = {v_{y0}} - gt$$

Here,

${v_x}$ is the velocity along x-axis,

${v_{x0}}$ is the initial velocity along x-axis,

${v_y}$ is the velocity along y-axis,

${v_{y0}}$ is the initial velocity along y-axis.

$g$ is the acceleration due to gravity and

$t$ is the time taken.

**Time of flight**$$t = {{2{v_o}\sin \theta } \over g}$$

**Maximum height reached**$$H = {{v_0^2{{\sin }^2}\theta } \over {2g}}$$

**Horizontal range**$$R = {{v_0^2\sin 2\theta } \over g}$$

Here,

$v_{0}$ is the initial Velocity,

${\sin \theta }$ is the component along y-axis,

${\cos \theta }$ is the component along x-axis.

### Uniform circular motion

**Angular velocity**$$\omega = {{d\theta } \over {dt}}$$

where $\theta$ is angle moved in radian's

**Relation between linear velocity, angular velocity and radius of circular motion**$$v=r\omega$$

**Angular acceleration**$$\alpha = {{d\omega } \over {dt}}$$

**Centripetal acceleration**$${a_c} = {{{v^2}} \over r}$$ $${{\vec a}_c} = - {\omega ^2}\vec r$$

Get kinematics equation list as pdf (opens in new window)

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