Physics Examples

$K = \frac{1}{2} m v^{2}$

Step 1

Substitute the given values into $K = \frac{1}{2} m v^{2}$ .

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Step 1.1

Substitute $2.5 kg$ for $m$ .

$K = \frac{1}{2} (2.5 kg) v^{2}$

Step 1.2

Substitute $1 \frac{m}{s}$ for $v$ .

$K = \frac{1}{2} (2.5 kg) {(1 \frac{m}{s})}^{2}$

$K = \frac{1}{2} (2.50 kg) {(1.00 \frac{m}{s})}^{2}$

Step 2

Simplify the right side.

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Step 2.1

Simplify.

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Step 2.1.1

Combine $\frac{1}{2}$ and $2.50 kg$ .

$K = \frac{2.50}{2} kg {(1.00 \frac{m}{s})}^{2}$

Step 2.1.2

Divide $2.50$ by $2$ .

$K = 1.25 kg {(1.00 \frac{m}{s})}^{2}$

Step 2.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.2.1

Apply the product rule to $1.00 \frac{m}{s}$ .

$K = 1.25 kg ({1.00}^{2} {(\frac{m}{s})}^{2})$

Step 2.2.2

Apply the product rule to $\frac{m}{s}$ .

$K = 1.25 kg ({1.00}^{2} \frac{m^{2}}{s^{2}})$

Step 2.3

Combine fractions.

$K = 1.25 kg \frac{m^{2}}{s^{2}}$

Step 2.4

Combine $1.25 kg$ and $\frac{m^{2}}{s^{2}}$ .

$K = 1.25 \frac{kg m^{2}}{s^{2}}$

Step 2.5

Rewrite $\frac{kg m^{2}}{s^{2}}$ as $J$ .

$K = 1.25 J$

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