Physics Examples

$\overline{a} = \frac{v - v_{0}}{t}$

$\overline{a}$	$=$	$?$
$v$	$=$	$42 \frac{km}{s}$
$v_{0}$	$=$	$2 \frac{km}{s}$
$t$	$=$	$2 \cdot 10^{3} s$

Step 1

Substitute the given values into $\overline{a} = \frac{v - v_{0}}{t}$ .

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Step 1.1

Substitute $42 \frac{km}{s}$ for $v$ .

$\overline{a} = \frac{42 \frac{km}{s} - v_{0}}{t}$

Step 1.2

Substitute $2 \frac{km}{s}$ for $v_{0}$ .

$\overline{a} = \frac{42 \frac{km}{s} - (2 \frac{km}{s})}{t}$

Step 1.3

Substitute $2 \cdot 10^{3} s$ for $t$ .

$\overline{a} = \frac{42 \frac{km}{s} - (2 \frac{km}{s})}{2 \cdot 10^{3} s}$

$\overline{a} = \frac{42.0 \frac{km}{s} - (2.00 \frac{km}{s})}{2 \cdot 10^{3} s}$

Step 2

Simplify the right side.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Combine fractions.

$\overline{a} = \frac{42.0 \frac{km}{s} - 2.00 \frac{km}{s}}{2 \cdot 10^{3} s}$

Step 2.1.2

Subtract $2.00 \frac{km}{s}$ from $42.0 \frac{km}{s}$ .

$\overline{a} = \frac{40.00 \frac{km}{s}}{2 \cdot 10^{3} s}$

Step 2.2

Cancel the common factor of $40.00$ and $2$ .

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Step 2.2.1

Factor $2$ out of $40.00 \frac{km}{s}$ .

$\overline{a} = \frac{2 (20.00 \frac{km}{s})}{2 \cdot 10^{3} s}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $2 \cdot 10^{3} s$ .

$\overline{a} = \frac{2 (20.00 \frac{km}{s})}{2 (10^{3} s)}$

Step 2.2.2.2

Cancel the common factor.

$\overline{a} = \frac{2 (20.00 \frac{km}{s})}{2 (10^{3} s)}$

Step 2.2.2.3

Rewrite the expression.

$\overline{a} = \frac{20.00 \frac{km}{s}}{10^{3} s}$

Step 2.3

Raise $10$ to the power of $3$ .

$\overline{a} = \frac{20.00 \frac{km}{s}}{1000 s}$

Step 2.4

Cancel the common factor of $20.00$ and $1000$ .

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Step 2.4.1

Factor $20.00$ out of $20.00 \frac{km}{s}$ .

$\overline{a} = \frac{20.00 (1 \frac{km}{s})}{1000 s}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $20.00$ out of $1000 s$ .

$\overline{a} = \frac{20.00 (1 \frac{km}{s})}{20.00 (50 s)}$

Step 2.4.2.2

Cancel the common factor.

$\overline{a} = \frac{20.00 (1 \frac{km}{s})}{20.00 (50 s)}$

Step 2.4.2.3

Rewrite the expression.

$\overline{a} = \frac{1 \frac{km}{s}}{50 s}$

Step 2.5

Factor $\frac{km}{s}$ out of $\frac{1 \frac{km}{s}}{50 s}$ .

$\overline{a} = \frac{km}{s} \cdot \frac{1}{50 s}$

Step 2.6

Combine fractions.

$\overline{a} = \frac{1}{50} \frac{km}{s^{2}}$

Step 2.7

Divide $1$ by $50$ .

$\overline{a} = 0.02 \frac{km}{s^{2}}$

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