Conceptual Physics

1.9 - Sample problem: conversions

Variables

We will use a to represent the acceleration we are converting.

What is the strategy?

1. Express the car's acceleration in scientific notation.


2. Using conversion factors in scientific notation, convert miles to yards and then to meters.


3. Convert hours squared to minutes squared and then to seconds squared.


4. Go for the challenge! Convert to terameters.

Conversion factors and prefixes

1 mi = 1760 yd

1 yd = 0.914 m

1 h = 60 min

1 min = 60 s

tera = 10^12

Step-by-step solution

We first write the acceleration in scientific notation and convert miles to yards to meters.

Now we convert hours squared to minutes squared to seconds squared. Because the units we are converting are squared, we square the
conversion factors. As requested, we state the final result in scientific notation.

Express the car's acceleration in

m/s^2 , using scientific notation. For an

extra challenge, state the result in

terameters per second squared.

Step Reason

1. a = 9430 mi/h^2 = 9.43×10^3 mi/h^2 scientific notation

2. multiply by factor converting miles to yards

3. multiply by factor converting yards to meters

Step Reason

4. multiply by square of factor converting hours to minutes

5. multiply by square of factor converting minutes to seconds

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