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).

Contents

## 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)

$$v = {v_0} + at$$ $$x = {x_0} + {v_0} + {1 \over 2}a{t^2}$$ $${v^2} = {v_0}^2 + 2a(x – {x_0})$$ $$\overline v = {1 \over 2}(v + {v_0})$$

### 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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