v.1. Equations of Motion: Understanding the Dynamics of Velocity, Acceleration, and Distance in Linear Motion
When an object travels in a straight line and experiences uniform acceleration, it abides by certain relationships between its various motion attributes: velocity, acceleration, and the distance covered. These relationships are captured in a set of equations commonly referred to as the “equations of motion”.
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Three Primary Equations of Motion: |
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Velocity-Time Relation: |
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Position-Time Relation: |
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Position-Velocity Relation: |
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In the equations:
- u stands for the initial velocity.
- v denotes the final velocity after time t.
- a is the uniform acceleration.
- s is the distance or displacement covered during the time t.
- Framework: These equations provide a foundational framework for analyzing linear motion with uniform acceleration.
- Graphical representation: Notably, they can be derived using graphical methods, illustrating the power of graphical representations in understanding and deriving physical relationships.
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Example: A car accelerates uniformly from 18 km h–1 to 36 km h–1 in 5s. Calculate (i) the acceleration and (ii) the distance covered by the car in that time. Solution: We are given that u = 18 km h–1 =5ms–1 v= 36 km h–1 =10ms–1 and t= 5s. (i) a = v–u / t = 10ms-1 – 5ms-1 / 5s (ii) s = ut + ½ at2 = 5ms–1 × 5s + ½ × 1 ms–2 × (5 s)2 = 25 m + 12.5 m = 37.5 m |