Question

A speed of \(7 \mathrm{~mm} / \mu \mathrm{s}\) is equal to: a) \(7000 \mathrm{~m} / \mathrm{s}\) b) \(70 \mathrm{~m} / \mathrm{s}\) c) \(7 \mathrm{~m} / \mathrm{s}\) d) \(0.07 \mathrm{~m} / \mathrm{s}\)

Short answer

Question: Convert the given speed, \(7 \mathrm{~mm} / \mu \mathrm{s}\), to meters per second, and match the result to one of the following options: a) \(7000 \mathrm{~m} / \mathrm{s}\), b) \(0.007 \mathrm{~m} / \mathrm{s}\), c) \(7 \times 10^6 \mathrm{~m} / \mathrm{s}\), d) \(7 \mathrm{~m} / \mathrm{s}\). Answer: a) \(7000 \mathrm{~m} / \mathrm{s}\)

Step-by-step solution

Write down the given speed and conversion factors

The given speed is \(7 \mathrm{~mm} / \mu \mathrm{s}\). We need to convert it to meters per second by using the following conversion factors: 1) 1 millimeter (mm) = 0.001 meters (m) 2) 1 microsecond (\(\mu\)s) = \(10^{-6}\) seconds (s)

Convert the given speed to meters per second

To convert the speed, we need to multiply the given speed by the conversion factors for both millimeters to meters and microseconds to seconds. \(\frac{7 \mathrm{~mm}}{\mu \mathrm{s}} \times \frac{0.001 \mathrm{~m}}{1 \mathrm{~mm}} \times \frac{1 \mathrm{s}}{10^{-6} \mathrm{~s}}\)

Simplify the expression

Now we simplify the expression by canceling out the units (mm, \(\mu\)s) and doing the multiplication: \(7 \times 0.001 \mathrm{~m} \times 10^6 \mathrm{~s} = 7 \times 10^3 \mathrm{~m} / \mathrm{s}\)

Match the answer to the given options

Now that we have found the equivalent speed in meters per second, we need to match it to the given options. The result we found is: \(7 \times 10^3 \mathrm{~m} / \mathrm{s} = 7000 \mathrm{~m} / \mathrm{s}\) Matching our result to the given options, we find that the correct answer is: a) \(7000 \mathrm{~m} / \mathrm{s}\)

Key concepts

Speed Conversion in Physics

Understanding speed conversion is crucial in physics as it allows us to compare and analyze motion in different units. For instance, converting speed from millimeters per microsecond to meters per second involves multiplying by appropriate conversion factors.

To convert, we use the conversion factors that 1 millimeter (mm) is equivalent to 0.001 meters (m) and 1 microsecond (\(\mu\)s) is equivalent to \(10^{-6}\) seconds (s). By performing the necessary multiplication, we achieve a consistent speed measurement across different units, which is paramount in relating real-world phenomena with theoretical physics calculations.

Why is Consistent Units Important?

It's vital for physical calculations to be in consistent units to avoid significant errors. Converting speeds allows us to seamlessly compare results from different systems or scales, ensuring accurate and meaningful conclusions in studies of motion.

Measurement Units in Physics

Measurement units are the backbone of scientific communication, allowing us to quantify and communicate the properties and behaviors of the physical world. Physics commonly uses the International System of Units (SI), which includes meters for distance, seconds for time, and meters per second for speed.

Converting between units, like mm to m and microseconds to seconds, is a routine practice in physics problem-solving. This process guarantees that all measurements are in base units, the standard units of measurement that form the foundation for all other units, hence creating a common ground for comparison and analysis.

The Importance of Base Units

Base units facilitate communication and collaboration across scientific disciplines, ensuring that everyone speaks the same 'measurement language'. This clarity is pivotal in advancing our understanding of physical phenomena.

Physics Problem Solving

Effective problem-solving in physics involves a step-based approach to systematically tackle exercises, such as the speed conversion problem presented.

Step 1 usually starts with identifying the given information and determining what you are solving for. Step 2 involves selecting the appropriate conversion factors, while Step 3 requires algebraic manipulation to convert and simplify the units. Finally, in Step 4, you compare your result with the available options to find the correct answer.

Developing a Systematic Approach

Practicing this method develops a student's ability to approach problems logically and consistently, leading to better understanding and mastery of physics concepts. To enhance learning, it's often helpful to 'translate' the problem into a real-world context or visualize the process to anchor abstract concepts into tangible examples.