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Electric drag racers rely on constant acceleration to achieve high speeds over a short distance. Constant acceleration means the velocity of the drag racer increases steadily over time. In our exercise, the acceleration remains the same from start to finish, regardless of the racer's speed at any given moment. This simplifies calculations and makes it easier to predict the elapsed time over a certain distance.
The formula we'll use to explore this is \[ s = ut + \frac{1}{2}at^2 \] where:

• \( s \) is the distance traveled,
• \( u \) is the initial velocity (zero in our example),
• \( a \) is the acceleration,
• \( t \) is the time.

This equation helps us solve for acceleration \( a \) when time and distance are known, establishing a foundation for understanding motion in physics.

In physics, comparing different forms of acceleration can offer valuable insight into their relative strength. Here, we compare the electric drag racer's acceleration to the acceleration due to gravity.
The standard acceleration due to gravity on Earth is \( 9.81 \text{ m/s}^2 \). In our case, we calculated the racer's acceleration to be \( 8.045 \text{ m/s}^2 \). This means that the racer accelerates a bit more slowly than free-falling objects drawn by gravity.
These comparisons help us understand how rapid the change in velocity is for electric drag racers, placing it in the context of a natural force all of us are familiar with—gravity. It also highlights just how powerful these vehicles are, coming close to a natural force that influences everything on Earth.

When solving physics problems, converting units is often necessary to make your calculations consistent and meaningful. In this exercise, we needed to convert the distance from miles to meters to use the standard units in physics equations.
Since 1 mile roughly equals 1609 meters, converting a quarter-mile distance gives us approximately 402.25 meters. This allows us to employ consistent units when using equations for motion, such as \( s = \frac{1}{2}at^2 \).
Later, we had to convert the final speed from meters per second (\text{m/s\}) to miles per hour (\text{mi/h\}). This conversion used the factor \( 1 \text{ m/s} = 2.237 \text{ mi/h} \).
Accurate unit conversion is crucial as it ensures that our calculations reflect real-world measurements, providing us with results that are universally understood.

To determine how fast the electric drag racer is traveling at the quarter-mile mark, we calculate its final speed. This uses the equation \[ v = u + at \] where:

• \( v \) is the final velocity,
• \( u \) is the initial velocity (zero in this scenario),
• \( a \) is the acceleration,
• \( t \) is the time elapsed.

Plugging in our values, we find \( v = 80.45 \text{ m/s} \).
We convert this speed into miles per hour for better relatability, resulting in approximately \( 179.95 \text{ mi/h} \). This final speed demonstrates the incredible power of electric drag racers, capable of reaching such elevated velocities in just ten seconds.