In daily life, many objects move with changing speed such as a car starting from rest, a bus applying brakes, or a stone falling freely. To study such motion scientifically, we use kinematic equations or equations of motion. These equations describe the motion of an object moving in a straight line with uniform acceleration.
They help us calculate unknown physical quantities like velocity, displacement, acceleration, and time when some values are already known. Instead of solving by trial and error, these formulas give direct mathematical relationships between the variables.
Important physical quantities:
Before solving problems, we must understand the symbols used:
- \(u\ =\) Initial velocity
(velocity of the object at the beginning) - \(v\ =\) Final velocity
(velocity after some time) - \(a\ =\) Acceleration
(rate of change of velocity) - \(t\ =\) Time taken
- \(s\ =\) Displacement
(distance moved in a particular direction)
These five quantities are related through equations of motion.
Conditions for using equations of motion
These equations are applicable only when:
Motion is in a straight line
Acceleration is uniform (constant)
Quantities are measured in proper \(SI\) \(units\)
Acceleration is uniform (constant)
Quantities are measured in proper \(SI\) \(units\)
They are not directly used for irregular motion where acceleration changes continuously.
First equation of motion:
\( v-u+at\)
Meaning:
Final velocity depends on initial velocity and the change caused by acceleration over time.
Used to Find:
- Final velocity
- Initial velocity
- Acceleration
- Time
Example:
A car starts from rest and accelerates at \(3\) \(ms^{-2}\) for \(4\) \(s\).
Second equation of motion:
\(s=ut+\frac{1}{2}at^{2}\)
Meaning:
Displacement depends on:
- Distance covered due to initial velocity (\(ut\))
- Additional distance due to acceleration (\(\frac{1}{2}at^{2}\))
Used to Find:
- Displacement
- Time
- Acceleration
Example:
A bike moving at \(10\) \(m/s\) accelerates for \(5\) \(s\).
Third equation of motion:
\( v^{2}=u^{2}+2as\)
Meaning:
This equation connects velocity, acceleration, and displacement directly.
Used when:
- Time is not given
- Need to find acceleration or stopping distance
Example:
A train moving at \(20\) \(m/s\) stops after applying brakes.
How to Select the Correct Equation
Step \(1\): Identify the known values
Write values of: \(u\), \(v\), \(a\), \(t\), \(s\)
Step \(2\): Identify the unknown quantity
Step \(3\): Choose equation containing only one unknown.
Quick revision table:
| Situation | Best equation |
| Need final velocity | \( v-u+at\) |
| Need displacement with time | \(s=ut+\frac{1}{2}at^{2}\) |
| Time missing | \(v^{2}=u^{2}+2as\) |
Revision table