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First Equation of Motion
The first equation connects initial velocity, final velocity, acceleration and time: v = u + at. It does not contain displacement.
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First Equation of Motion
7. First Equation
The first equation connects:
- Initial velocity
- Final velocity
- Acceleration
- Time
It does not contain displacement. v = u + at
8. Derivation of the First Equation
Acceleration is defined as: a = (change in velocity) / time a = v − ut Multiplying both sides by t: at = v − u Adding u to both sides: u + at = v Therefore: v = u + at
9. Meaning of the First Equation
The change in velocity during time t is: Δv = at Therefore: Final velocity = Initial velocity + Change in velocity v = u + at If acceleration is negative, velocity decreases with time.
10. Solved Example 1: Finding Final Velocity
Solved Example 1: Finding Final Velocity
A car has an initial velocity of 10 m s⁻¹. It accelerates uniformly at 2 m s⁻² for 5 s. Find its final velocity.
- u = 10 m s⁻¹
- a = 2 m s⁻²
- t = 5 s
- Required: v = ?
- Formula: v = u + at
v = 10 + (2)(5)
v = 10 + 10
v = 20 m s⁻¹
Final answer: v = 20 m s⁻¹
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Practice
Practice
Q1. A car starts from rest and accelerates at 4 m s⁻² for 6 s. Find its final velocity.
Practice
Q2. An object is dropped for 4 s. Find its final velocity using g = 10 m s⁻².
Practice
Q3. An object falls from rest through 80 m. Find its time and final velocity using g = 10 m s⁻².