Physics Examples

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

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

$K$ $K$	$=$ $=$	$?$ $?$
$m$ $m$	$=$ $=$	$2.5 kg$ $2.5 kg$
$v$ $v$	$=$ $=$	$1 \frac{m}{s}$ $1 \frac{m}{s}$

Step 1

Substitute the given values into

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

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

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Step 1.1

Substitute

2.5 kg

$2.5 kg$ for

m

$m$ .

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

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

Step 1.2

Substitute

1 \frac{m}{s}

$1 \frac{m}{s}$ for

v

$v$ .

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

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

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

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

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}

$\frac{1}{2}$ and

2.50 kg

$2.50 kg$ .

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

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

Step 2.1.2

Divide

2.50

$2.50$ by

2

$2$ .

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

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

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

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

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Step 2.2.1

Apply the product rule to

1.00 \frac{m}{s}

$1.00 \frac{m}{s}$ .

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

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

Step 2.2.2

Apply the product rule to

\frac{m}{s}

$\frac{m}{s}$ .

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

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

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

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

Step 2.3

Combine fractions.

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

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

Step 2.4

Combine

1.25 kg

$1.25 kg$ and

\frac{m^{2}}{s^{2}}

$\frac{m^{2}}{s^{2}}$ .

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

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

Step 2.5

Rewrite

\frac{kg m^{2}}{s^{2}}

$\frac{kg m^{2}}{s^{2}}$ as

J

$J$ .

K = 1.25 J

$K = 1.25 J$

K = 1.25 J

$K = 1.25 J$

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