The mass of a motorcyclist together with the motorcycle is 90 kg. Calculate the increase in kinetic energy if the speed increases from 6.0 km/h to 12 km/h.

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Points to Remember:

  • Kinetic energy is the energy of motion.
  • Kinetic energy is calculated using the formula: KE = 1/2 * mv² (where m is mass and v is velocity).
  • Units must be consistent (e.g., kilograms for mass, meters per second for velocity).

Introduction:

This question requires a factual and analytical approach to calculate the change in kinetic energy of a motorcycle and rider system. Kinetic energy, a fundamental concept in physics, is the energy possessed by an object due to its motion. The formula KE = ½mv² directly relates kinetic energy (KE) to the object’s mass (m) and velocity (v). This problem involves applying this formula to determine the change in kinetic energy when the velocity of a motorcycle and rider increases.

Body:

1. Converting Units:

Before applying the formula, we need to convert the speeds from kilometers per hour (km/h) to meters per second (m/s), the standard unit for velocity in the kinetic energy formula.

  • Initial speed: 6.0 km/h * (1000 m/km) * (1 h/3600 s) = 1.67 m/s
  • Final speed: 12 km/h * (1000 m/km) * (1 h/3600 s) = 3.33 m/s

2. Calculating Initial Kinetic Energy:

Using the formula KE = ½mv², we calculate the initial kinetic energy:

KE₁ = ½ * 90 kg * (1.67 m/s)² = 125.0 J (Joules)

3. Calculating Final Kinetic Energy:

Next, we calculate the kinetic energy at the increased speed:

KE₂ = ½ * 90 kg * (3.33 m/s)² = 499.0 J (Joules)

4. Determining the Increase in Kinetic Energy:

Finally, we find the difference between the final and initial kinetic energies to determine the increase:

Increase in KE = KE₂ – KE₁ = 499.0 J – 125.0 J = 374.0 J

Therefore, the increase in kinetic energy is 374 Joules.

Conclusion:

In conclusion, by applying the formula for kinetic energy and converting units appropriately, we determined that a 374 Joule increase in kinetic energy occurs when the speed of the 90 kg motorcycle and rider system increases from 6.0 km/h to 12 km/h. This calculation highlights the non-linear relationship between velocity and kinetic energy; doubling the speed quadruples the kinetic energy. This underscores the importance of safe riding practices and adherence to speed limits, as even small increases in speed can lead to significant increases in kinetic energy, impacting the severity of potential accidents. Further research could explore the relationship between kinetic energy and accident severity to inform road safety policies and driver education programs. Promoting responsible road usage through education and infrastructure improvements is crucial for holistic development and public safety.

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