Equations of motion
- Olympiad · NSEJS
The equations of motion are three formulas linking speed, time, distance and acceleration for a body moving in a straight line with steady acceleration.
Let u be the starting velocity, v the final velocity, a the acceleration, t the time and s the distance covered. For steady acceleration:
- v = u + at.
- s = ut + ½at².
- v² = u² + 2as.
Each one leaves out one quantity. Pick the equation that skips the thing you neither know nor need. All three come from a velocity-time graph. The slope of the graph is the acceleration, and the area under it is the distance.
A small example
A car starts from rest and speeds up at 2 m/s² for 5 s. Find its final speed and the distance it covers.
- Here u = 0, a = 2 m/s² and t = 5 s.
- v = 0 + 2 × 5 = 10 m/s.
- s = 0 × 5 + ½ × 2 × 5² = 25 m.
- Check with the third equation: v² = 0 + 2 × 2 × 25 = 100, so v = 10 m/s.
The equations only work when the acceleration stays the same. A body falling freely near the Earth is one such case. There, a is the acceleration due to gravity, which comes from the universal law of gravitation.
Where it fits
This goes beyond the Class 10 board syllabus. HBCSE's Junior Science syllabus lists it under motion. That syllabus is for NSEJS, which the Indian Association of Physics Teachers (IAPT) conducts.
Sources
Facts last checked against these sources on 30 September 2026.
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