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# Kinematics Formulas

Kinematics Formula is all about the motion of bodies at points, without considering the cause due to which it occurs.

There are three kinematic formulas namely:

Here,
xo and x are Initial and final displacements expressed in m,
vo and v are initial and final velocity expressed in m/s,
a is acceleration given in m/s2,
t is time taken in s.

2D Kinematics Formulas

2D or 2 dimensional kinematics equations is all about expressing the same equations in x and y directions:
In x direction the Kinematics formulas is given as:
vx = vxo + axt
x = xo + vxot + $\frac{1}{2}$ axt2
vx2 = vxo + 2ax(x-xo)

In y-direction the Kinematic formula is given as:
vy = vyo + ayt
y = xo + vyot + $\frac{1}{2}$ ayt2
vy2 = vyo2 + 2ay(y - yo).

Kinematics Formulas for Projectile Motion

Consider a projectile motion as shown in figure the kinematics formulas are:
In x-direction:
vx = vxo
x = xo + vxo
In y-direction:
vy = vyo - gt
y = yo + vyot - $\frac{1}{2}$ gt2
vy2 = vyo2 - 2g(y - yo)

 Related Calculators Kinematics Calculator Acceleration Formula Calculator Area of a Circle Formula Calculator Area of a Cylinder Formula Calculator

## Kinematics Problems

Below are solved Kinematics problems which helps you in understanding the use of these equations.

### Solved Examples

Question 1: A guy is riding a bike with initial velocity of 2 m/s. He reaches his destiny after 3s having final velocity of 10m/s. Calculate its acceleration?
Solution:

Given: Initial Velocity vo = 2 m/s
Final velocity v = 10 m/s
Time period t = 3s
To find the acceleration a
Using the formula v = vo + at
Acceleration is given as:
a = $\frac{v - v_{0}}{t}$
= $\frac{10m/s - 2m/s}{3s}$
= 2.67 m/s2.

Question 2: A car with initial velocity zero experiences uniform acceleration of 7 m/s2 for the time interval t= 5s. Calculate its distance covered?
Solution:

Initial Velocity vo = 0,
time taken t = 5s,
Acceleration a = 7 m/s2,
To find the Distance covered S.
By using the Kinematic Equation we can conclude that,
S = vot + $\frac{1}{2}$at2,
= (0) $\times$ (5)+ $\frac{1}{2}$ $\times$ 8 m/s2 (5)2
=100m.

 More topics in Kinematics Formulas Distance Speed Time Formula Displacement Formula Velocity Formula Acceleration Formula Momentum Formula Formula Dynamics Speed Distance Time Formula Rotational Inertia Formula Newton's Second Law Formula Circular Velocity Formula
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