📘 Numerical Problems (Kinematics)
Learn and understand the Numerical Problems of Chapter 2 – Kinematics from Class 9 Physics with step-by-step solutions. This page provides free downloadable numericals covering equations of motion, velocity calculations, acceleration problems, and free fall under gravity according to the Punjab PECTA 2025 syllabus.
Related Resources:
Introduction to Kinematics Numerical Problems
Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. Numerical problems in kinematics help us apply theoretical concepts to practical situations.
This section contains carefully selected numerical problems that cover all important concepts of kinematics. Solving these problems will help you:
- Understand the application of kinematic equations
- Develop problem-solving skills
- Prepare for exams with practical questions
- Build confidence in handling numerical calculations
- Connect theoretical concepts with real-world scenarios
Each problem is accompanied by a detailed step-by-step solution to help you understand the methodology and approach required to solve similar problems.
Important Formulas for Kinematics
Distance
\[S = v_{av} \times t\]Where \( S \) is distance, \( v_{av} \) is average speed, and \( t \) is time
Average Acceleration
\[a_{av} = \frac{v_f - v_i}{t}\]Where \( v_i \) is initial velocity, \( v_f \) is final velocity, and \( t \) is time
First Equation of Motion
\[v_f = v_i + at\]Relates final velocity with initial velocity, acceleration, and time
Second Equation of Motion
\[S = v_i t + \frac{1}{2} at^2\]Relates displacement with initial velocity, time, and acceleration
Third Equation of Motion
\[2aS = v_f^2 - v_i^2\]Relates velocity and displacement without time
Equations of Motion Under Gravity
\[v_f = v_i + gt\] \[h = v_i t + \frac{1}{2} gt^2\] \[2gh = v_f^2 - v_i^2\]For free fall, \( g \) is positive; for upward motion, \( g \) is negative
Important Conversion Factors:
To convert \( ms^{-1} \) to \( kmh^{-1} \) multiply speed with 3.6
To convert \( kmh^{-1} \) to \( ms^{-1} \) multiply speed with \( \frac{10}{36} \)
Problem Solving Approach
Step 1: Identify Given Data - Carefully read the problem and list all given quantities with their units.
Step 2: Identify Required Quantity - Determine what needs to be found in the problem.
Step 3: Select Appropriate Formula - Choose the kinematic equation that connects the given and required quantities.
Step 4: Unit Conversion - Ensure all quantities are in consistent units (preferably SI units).
Step 5: Substitute and Solve - Plug the values into the formula and solve for the unknown.
Step 6: Check Your Answer - Verify that the answer makes physical sense and has correct units.
Created by Hira Science Academy | Aligned with PECTA 2025 Syllabus