Question Video: Using Formulae to Derive Units

The force applied on an object is calculated using the formula 𝐹 = 𝑚𝑎, where 𝑎 is the acceleration of the object (measured in metres per second squared, or m/s²) and 𝑚 is its mass (measured in kilograms, or kg). The force is then measured in newtons. Which of the following is the expression of newtons in terms of the base units kilograms, metres, and seconds? [A] kg⋅m/s² [B] (kg⋅m/s)² [C] kg⋅s²/m [D] kg⋅m/s [E] kg⋅m²/s².

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Video Transcript

The force applied on an object is calculated using the formula 𝐹 equals 𝑚𝑎, where 𝑎 is the acceleration of the object measured in metres per second squared and 𝑚 is the mass measured in kilograms. The force is then measured in newtons. Which of the following is the expression of newtons in terms of the base units kilograms, metres, and seconds? Is it a) kilograms multiplied by metres per second squared? Is it b) kilograms multiplied by metres per second all squared? Is it c) kilograms multiplied by seconds squared per metre, d) kilograms multiplied by metres per second, or e) kilograms multiplied by metres squared per second squared?

Let’s first consider the formula 𝐹 equals 𝑚𝑎. This means that the force is equal to the mass multiplied by the acceleration. Well, our units for mass are kilograms. Therefore, the first term must be kilograms. The units for acceleration are metres per second squared. Therefore, the second term must be metres per second squared.

This means that the expression must be kilograms multiplied by metres per second squared. Well, in this case, option a says kilograms multiplied by metres per second squared. Therefore, the expression for newtons in terms of the base units kilograms, metres, and seconds is kilograms multiplied by metres per second squared.

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