Understanding Uniform Acceleration in a Real-World Scenario: A Car's Velocity after 5 Minutes

In this article, we will explore a real-world problem involving a car's velocity after a period of uniform acceleration. Uniform acceleration is a crucial concept in physics and engineering, which addresses the change in velocity over time under constant acceleration. This article will break down the math involved to achieve an accurate understanding.

Problem: A Car Accelerating at a Uniform Rate

The problem at hand is: A car initially traveling at 50 km/h accelerates uniformly at 6 m/s2. What will be its velocity after 5 minutes?

Step-by-Step Solution

Step 1: Convert Units

First, we need to convert all the units to the standard units used in physics. This includes converting the initial velocity from kilometers per hour to meters per second.

Initial velocity (u): 50 km/h to m/s

u 50 , text{km/h} times frac{1000 , text{m}}{1 , text{km}} times frac{1 , text{h}}{3600 , text{s}} frac{50000}{3600} approx 13.89 , text{m/s}

The car's initial velocity is approximately 13.89 m/s.

Step 2: Identify Given Values and Required Values

Acceleration (a): 6 m/s2, already in the correct units.

Time (t): 5 minutes to seconds

t 5 , text{minutes} times 60 , text{s/minute} 300 , text{s}

Step 3: Apply the Uniform Acceleration Formula

Using the formula for final velocity with uniform acceleration:

v u at

Substitute the known values:

v 13.89 , text{m/s} 6 , text{m/s}^2 times 300 , text{s} 13.89 , text{m/s} 1800 , text{m/s} 1813.89 , text{m/s}

Final Answer

The final velocity of the car after 5 minutes is approximately 1813.89 meters per second.

Discussion and Real-World Application

Let's break down the solution further for clarity and practical understanding. The car starts at 13.89 m/s and accelerates to 1813.89 m/s. This is a significant speed increase, equivalent to about 6530 km/h if we consider the total increase in velocity.

Initial speed Final speed increase 13.89 , text{m/s} 1800 , text{m/s} approx 1813.89 , text{m/s}

1813.89 , text{m/s} times frac{3600 , text{s/hour}}{1000 , text{m/km}} 6530 , text{km/h}

The car's increase in speed would be 6530 km/h. If this increase in speed is not accounted for in the initial speed (50 km/h), the total speed would be 6580 km/h, considering the initial speed.

Implications and Considerations

When dealing with such high speeds, it is important to consider:

Road safety and legal limits. Aerodynamic drag and fuel efficiency. Braking distance and maneuverability.

For vehicles to achieve such high speeds, they would need highly efficient engines, advanced aerodynamics, and potentially specialized technology. However, the laws of physics and engineering limit such capabilities to specialized vehicles, such as those used in racing or experimental research.

Conclusion

In conclusion, understanding uniform acceleration is essential for both theoretical physics and practical applications in engineering. The problem illustrated in this article shows the significant impact of even moderate acceleration rates over time.