Physics Equations Kinematics

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.

$${a_{avg}} = {{\Delta v} \over {\Delta t}} Instantaneous acceleration$$a = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta v} \over {\Delta t}} = {{dv} \over {dt}}$$Equations of motion (constant acceleration)$$v = {v_0} + atx = {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} + gtx = {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)