There are three kinematic formulas namely:

Here,

**x**_{o} and **x** are Initial and final displacements expressed in **m**,

**v**_{o} and **v** are initial and final velocity expressed in **m/s**,

**a** is acceleration given in **m/s**^{2},

**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:

**Kinematics Formulas for Projectile Motion**

Consider a projectile motion as shown in figure the kinematics formulas are:

In x-direction:

In x direction the Kinematics formulas is given as:

v_{x} = v_{xo} + a_{x}t

x = x_{o} + v_{xo}t + $\frac{1}{2}$ a_{x}t^{2}

v_{x}^{2} = v_{x}o + 2ax(x-x_{o})

In y-direction the Kinematic formula is given as:x = x

v

v_{y} = v_{yo} + a_{y}t

y = x_{o} + v_{yo}t + $\frac{1}{2}$ a_{y}t^{2}

v_{y}^{2} = v_{yo}^{2 }+ 2ay(y - y_{o}).

y = x

v

Consider a projectile motion as shown in figure the kinematics formulas are:

In x-direction:

v_{x} = v_{xo}

x = x_{o} + v_{xo}

In y-direction:x = x

v_{y }= v_{yo} - gt

y = y_{o} + v_{yo}t - $\frac{1}{2}$ gt^{2}

v_{y}^{2} = v_{yo}^{2} - 2g(y - y_{o})

y = y

v

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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 v_{o} = 2 m/s

Final velocity v = 10 m/s

Time period t = 3s

To find the acceleration a

Using the formula v = v_{o} + at

Acceleration is given as:

a = $\frac{v - v_{0}}{t}$

= $\frac{10m/s - 2m/s}{3s}$

= 2.67 m/s^{2}.

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

** Solution: **

Initial Velocity v_{o} = 0,

time taken t = 5s,

Acceleration a = 7 m/s^{2},

To find the Distance covered S.

By using the Kinematic Equation we can conclude that,

S = v_{o}t + $\frac{1}{2}$at^{2},

= (0) $\times$ (5)+ $\frac{1}{2}$ $\times$ 8 m/s^{2} (5)^{2}

=100m.

Given: Initial Velocity v

Final velocity v = 10 m/s

Time period t = 3s

To find the acceleration a

Using the formula v = v

Acceleration is given as:

a = $\frac{v - v_{0}}{t}$

= $\frac{10m/s - 2m/s}{3s}$

= 2.67 m/s

Initial Velocity v

time taken t = 5s,

Acceleration a = 7 m/s

To find the Distance covered S.

By using the Kinematic Equation we can conclude that,

S = v

= (0) $\times$ (5)+ $\frac{1}{2}$ $\times$ 8 m/s

=100m.