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Equations of Motion
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Solve all three equations of motion with step-by-step AI solutions. Enter any known values and instantly find the unknown.
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1st Equation: v = u + at
Solve for: final velocity, initial velocity, acceleration, or time
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✅ Result
v = u + at
FINAL VELOCITY
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m/s
Step-by-Step Solution
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1st Equation of Motion
Relates final velocity to initial velocity, acceleration and time. Used when displacement is not required.
v = u + at
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2nd Equation of Motion
Gives displacement in terms of initial velocity, time and acceleration. Derived by integrating velocity.
s = ut + ½at²
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3rd Equation of Motion
Connects velocity and displacement without time. Most useful in projectile & free-fall problems.
v² = u² + 2as
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Derivation Summary
How each equation is derived
1
From definition of acceleration: a = (v−u)/t → rearranging gives v = u + at
2
Average velocity = (u+v)/2. Displacement = avg velocity × time → s = ut + ½at²
3
Eliminate t from 1st & 2nd equations → v² = u² + 2as (time-independent equation)
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All three equations are valid only for uniform acceleration (constant a) in a straight line.
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Variables & Symbols
All symbols used in equations of motion
| Symbol | Quantity | SI Unit | Type | Notes |
|---|---|---|---|---|
| v | Final Velocity | m/s | Vector | Velocity at end of motion |
| u | Initial Velocity | m/s | Vector | Velocity at start of motion |
| a | Acceleration | m/s² | Vector | Must be constant (uniform) |
| t | Time | s | Scalar | Duration of motion |
| s | Displacement | m | Vector | Straight-line distance |
| g | Gravity | 9.81 m/s² | Vector | Use 10 m/s² for NCERT |
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