Lecture Notes: Average Braking Force

Introduction

• Topic: Calculating average braking force
• Context: When driving a car and needing to stop at a signal
• Key Questions:
  • How long does it take to stop the car?
  • How much force is applied to stop the car?

Problem Setup

• Car Specifications:
  • Mass of the car: 1500 kg
  • Initial velocity (U): 30 m/s
  • Distance to stop (S): 550 meters
  • Final velocity (V): 0 m/s (car comes to a complete stop)

Calculating Acceleration

• Kinematic Equation Used:
  • ( V^2 = U^2 + 2aS )
• Substituting known values:
  • ( V = 0 ), ( U = 30 ), ( S = 550 )
• Solving for acceleration (a):
  • ( a = \frac{0^2 - 30^2}{2 \times 550} = -0.82 ) m/s²
• Interpretation of Negative Acceleration:
  • Negative sign indicates that acceleration is in the opposite direction to velocity (car is decelerating)

Calculating Average Braking Force

• Newton’s Second Law:
  • Force (F) = mass (m) × acceleration (a)
• Substituting values:
  • Mass = 1500 kg, Acceleration = -0.82 m/s²
• Calculation:
  • Force = 1500 kg × 0.82 m/s²
  • Result: 1230 N
• Interpretation of Negative Force:
  • Indicates the force is applied in the opposite direction of motion

Calculating Time to Stop

• Kinematic Equation Used:
  • ( V = U + at )
• Substituting known values:
  • ( V = 0 ), ( U = 30 ), ( a = -0.82 )
• Solving for time (t):
  • ( 0 = 30 + (-0.82)t )
  • ( t = \frac{30}{0.82} = 36.6 ) seconds

Alternative Equation

• Quadratic Equation Option:
  • ( S = Ut + \frac{1}{2}at^2 )
  • More complex due to being a quadratic equation

Conclusion

• Process to calculate braking force and time is straightforward
• Ensure understanding of negative signs in calculations
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