Physics Formula Kinematics

Kinematics Formulas in Physics: Complete Guide with Examples

What is Kinematics in Physics?

Kinematics is a branch of physics that deals with the motion of objects without considering the forces causing the motion. It focuses on quantities like displacement, velocity, acceleration, and time. Understanding kinematics is essential for solving real-world problems related to motion.

Key Kinematics Formulas

Here are the essential kinematics formulas, also known as the equations of motion:

1. First Equation of Motion: \( v = u + at \)

Where:
\( v \): Final velocity (m/s)
\( u \): Initial velocity (m/s)
\( a \): Acceleration (m/s²)
\( t \): Time (s)

2. Second Equation of Motion: \( s = ut + \frac{1}{2}at^2 \)

Where:
\( s \): Displacement (m)

3. Third Equation of Motion: \( v^2 = u^2 + 2as \)

This formula is useful when time is not involved.

4. Average Velocity: \( v_{\text{avg}} = \frac{u + v}{2} \)
5. Displacement for Constant Velocity: \( s = vt \)

Step-by-Step Examples

Example 1: Calculating Final Velocity

A car starts from rest and accelerates at \( 3 \, \text{m/s}^2 \) for 5 seconds. What is its final velocity?

Solution:
Given:
\( u = 0 \, \text{m/s}, \, a = 3 \, \text{m/s}^2, \, t = 5 \, \text{s} \)
Using \( v = u + at \):
\( v = 0 + (3 \times 5) = 15 \, \text{m/s} \)
Final velocity = 15 m/s

Example 2: Determining Displacement

A train moving at \( 20 \, \text{m/s} \) accelerates uniformly at \( 2 \, \text{m/s}^2 \) for 10 seconds. How far does it travel during this time?

Solution:
Given:
\( u = 20 \, \text{m/s}, \, a = 2 \, \text{m/s}^2, \, t = 10 \, \text{s} \)
Using \( s = ut + \frac{1}{2}at^2 \):
\( s = (20 \times 10) + \frac{1}{2}(2)(10^2) \)
\( s = 200 + 100 = 300 \, \text{m} \)
Displacement = 300 m

Example 3: Using the Third Equation

A cyclist starts at \( 10 \, \text{m/s} \) and accelerates at \( 4 \, \text{m/s}^2 \) until reaching a velocity of \( 30 \, \text{m/s} \). Find the displacement during this motion.

Solution:
Given:
\( u = 10 \, \text{m/s}, \, v = 30 \, \text{m/s}, \, a = 4 \, \text{m/s}^2 \)
Using \( v^2 = u^2 + 2as \):
\( 30^2 = 10^2 + 2(4)s \)
\( 900 = 100 + 8s \)
\( 800 = 8s \)
\( s = 100 \, \text{m} \)
Displacement = 100 m