Kinematics is that part of physics which deals with the study of motion, without necessarily going into the agencies producing the motion. Following are the important kinematic equations used to solve problems in which acceleration is constant. These equations relate displacement, velocity, acceleration, and time.
Table of Contents
Key Variables:
- d = Displacement (m)
- v₀ = Initial velocity (m/s)
- v = Final velocity (m/s)
- a = Acceleration (m/s²)
- t = Time (s)
The Four Key Kinematic Equations:
1. First Equation: (Final Velocity)
\[v = v₀ + at\]
It’s Usage: This formula is used to calculate final velocity of an object with given initial velocity, acceleration, and time.
2. Second Equation: (Displacement with Time)
\[d = v₀t + \frac{1}{2} a t^2\]
It’s Usage: If you know the the initial velocity, acceleration, and time, this formula is used to calculate the displacement of an object.
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3. Third Equation: (Displacement with Velocities)
\[d = \frac{v + v₀}{2} t\]
It’s Usage: If you know the time and both initial and final velocities, this formula is used to calculate the displacement of an object without requiring acceleration.
4. Fourth Equation: (Velocity-Displacement Relation)
\[v^2 = v₀^2 + 2ad\]
It’s Usage: This formula is used to calculate the final velocity without time.
Key Points:
- All units should be consistent. For example, meters for displacement and seconds for time.
- Acceleration should remain constant when using these equations.
- When solving, write down all known variables first and clearly identify what is missing.
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Essential Reminders:
- If the object starts from rest, v₀ = 0.
- If the object comes to rest, v = 0.
- For free-falling objects, use a = -9.8 m/s² (on Earth).
Using these equations in an organized way, it will help you solve many problems and questions related to motion with ease. Follow this process and take a look at key points mentioned above to improve your equation solving skills.
Kinematic Equations Formula Sheet PDF
We have also prepared a PDF which contains all the kinematic equations formula sheet and its uses also.
