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 $20 kg$ for $m$ .

$K = \frac{1}{2} (20 kg) v^{2}$

Step 1.2

Substitute $4 \frac{m}{s}$ for $v$ .

$K = \frac{1}{2} (20 kg) {(4 \frac{m}{s})}^{2}$

$K = \frac{1}{2} (20.0 kg) {(4.00 \frac{m}{s})}^{2}$

Step 2

Simplify the right side.

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Step 2.1

Combine $20.0$ and $\frac{1}{2}$ .

$K = \frac{20.0}{2} kg {(4.00 \frac{m}{s})}^{2}$

Step 2.2

Divide $20.0$ by $2$ .

$K = 10.0 kg {(4.00 \frac{m}{s})}^{2}$

Step 2.3

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

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Step 2.3.1

Apply the product rule to $4.00 \frac{m}{s}$ .

$K = 10.0 kg ({4.00}^{2} {(\frac{m}{s})}^{2})$

Step 2.3.2

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

$K = 10.0 kg ({4.00}^{2} \frac{m^{2}}{s^{2}})$

Step 2.4

Combine fractions.

$K = 160.0 kg \frac{m^{2}}{s^{2}}$

Step 2.5

Combine $160.0 kg$ and $\frac{m^{2}}{s^{2}}$ .

$K = 160.0 \frac{kg m^{2}}{s^{2}}$

Step 2.6

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

$K = 160.0 J$

Step 3

Round to $3$ significant figures.

$K = 1.60 \cdot 10^{2} J$

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