Horizontal Motion in Classical Physics

Introduction to Mechanics

• Mechanics: A major topic in classical physics comprised of:
  • Kinematics: Developed by Galileo, focuses on the motion of objects without reference to forces.
  • Dynamics: Studies the effect of forces on the motion of objects.

Focus on Kinematics

• Study of one and two-dimensional motion using equations.
• Importance: Demonstrated that math could describe motion on Earth, revolutionizing beliefs post-Aristotle.
• Factors affecting motion on Earth: Friction, atmosphere, etc.

Kinematic Equations

• Variables: Displacement, velocity, acceleration (constant), and time.
• Subscript Zero: Indicates initial conditions.

Fundamental Equations

1. Velocity at time t:
   • [ v = v_0 + at ]
2. Position with respect to origin:
   • [ x = x_0 + v_0t + \frac{1}{2}at^2 ]
3. Relationship between velocity and displacement:
   • [ v^2 = v_0^2 + 2a(x - x_0) ]

Supplemental Equations

• Position as average velocity over time:
  • [ x = \bar{v}t ]
• Average velocity:
  • [ \bar{v} = \frac{v + v_0}{2} ]

Applying Kinematic Equations: Examples

Example 1: Car Acceleration

• Scenario: Car accelerates from rest with 2.5 m/s² for 10s.
• Calculation for Velocity:
  • Initial velocity ( v_0 = 0 )
  • ( v = 2.5 \times 10 = 25 ) m/s
• Calculation for Distance:
  • ( x = 0 + \frac{1}{2}(2.5)(10)^2 = 125 ) meters

Example 2: Car Deceleration

• Scenario: Car moving at 27 m/s decelerates at -8.4 m/s².
• Calculation for Time to Stop:
  • Final velocity ( v = 0 )
  • ( 0 = 27 + (-8.4)t ), ( t = 3.2 ) seconds
• Calculation for Braking Distance:
  • ( x = 27 \times 3.2 + \frac{1}{2}(-8.4)(3.2)^2 )
  • Distance ( x \approx 43 ) meters

Conclusion

• Kinematic equations are versatile and applicable to various moving objects.

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