Question

In 2005 , Jarno Trulli was the pole winner of the U.S. Grand Prix Race with a speed of \(133 \mathrm{mi}\) per hr. What was his speed in \(\mathrm{cm} / \mathrm{s}\) ?

Short answer

The speed was approximately 5945.49 cm/s.

Step-by-step solution

Convert miles to centimeters

1 mile is equal to 160934.4 centimeters. Multiply Jarno Trulli's speed by this conversion factor: \( 133 \text{ miles/hour} \times 160934.4 \text{ cm/mile} = 21404375.2 \text{ cm/hour} \)

Convert hours to seconds

There are 3600 seconds in one hour. To find the speed in centimeters per second, divide the result from Step 1 by 3600: \( 21404375.2 \text{ cm/hour} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} = 5945.493 \text{ cm/second} \)

Key concepts

conversion factors

Conversion factors are vital tools in unit conversion. They allow us to convert a measurement from one unit to another by multiplying by a fraction that represents the ratio between the two units. For example, in the given exercise, we convert miles to centimeters. We know that 1 mile equals 160934.4 centimeters. Thus, the conversion factor here is 160934.4 cm/mile. This method ensures we can handle conversions across different unit systems accurately.

To perform a unit conversion:

• Identify the units you are converting from and to.
• Use a conversion factor that relates these units.
• Multiply your original measurement by the conversion factor.

Always ensure that units cancel out appropriately, leaving you with the desired unit.

speed conversion

Speed conversion involves changing the units of speed from one set to another. For example, converting miles per hour (mi/hr) to centimeters per second (cm/s). It requires both distance and time unit conversions. In the current exercise, we first converted miles to centimeters using the conversion factor 160934.4 cm/mile.

For a speed conversion, follow these steps:

• Convert the distance units (miles to cm in this case).
• Convert the time units (hours to seconds in this case).
• Adjust your calculation so that the new units correctly reflect the speed conversion.

In our example, after converting 133 mi/hr to cm/hr, we then converted hours to seconds by dividing by 3600 seconds/hour, giving us the speed in cm/s.

dimensional analysis

Dimensional analysis is a technique used to check the consistency of units in calculations. It ensures that the final units make sense for the quantity being measured. This method involves treating units as algebraic quantities that can be canceled out during calculations.

Here's a step-by-step guide for dimensional analysis:

• Write down the given quantity and its units.
• Use conversion factors to change units, canceling out the old units step by step.
• Ensure the final units are correct and match the desired units.

In our exercise, dimensional analysis helps us convert Jarno Trulli's speed from miles per hour to centimeters per second by confirming that the units correctly cancel out, ensuring the calculation's validity.