Physics Examples

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

$\overline{a}$	$=$	$1.3 \frac{km}{s^{2}}$
$v$	$=$	$?$
$v_{0}$	$=$	$2 \frac{km}{s}$
$t$	$=$	$2 \cdot 10^{3} s$

Step 1

Solve for $v$ .

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Step 1.1

Rewrite the equation as $\frac{v - v_{0}}{t} = \overline{a}$ .

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

Step 1.2

Multiply both sides by $t$ .

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

Step 1.3

Simplify the left side.

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Step 1.3.1

Simplify $\frac{v - v_{0}}{t} t$ .

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Step 1.3.1.1

Cancel the common factor of $t$ .

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Step 1.3.1.1.1

Cancel the common factor.

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

Step 1.3.1.1.2

Rewrite the expression.

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

Step 1.3.1.2

Reorder $v$ and $- v_{0}$ .

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

Step 1.4

Add $v_{0}$ to both sides of the equation.

$v = \overline{a} t + v_{0}$

Step 2

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

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Step 2.1

Substitute $1.3 \frac{km}{s^{2}}$ for $\overline{a}$ .

$v = 1.3 \frac{km}{s^{2}} t + v_{0}$

Step 2.2

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

$v = 1.3 \frac{km}{s^{2}} t + 2 \frac{km}{s}$

Step 2.3

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

$v = 1.3 \frac{km}{s^{2}} (2 \cdot 10^{3} s) + 2 \frac{km}{s}$

$v = 1.30 \frac{km}{s^{2}} (2.00 \cdot 10^{3} s) + 2.00 \frac{km}{s}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cross cancel units.

$v = 1.30 \frac{km}{s^{2}} \frac{2.00 \cdot 10^{3} s}{1} + 2.00 \frac{km}{s}$

Step 3.1.2

Simplify the expression.

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Step 3.1.2.1

Remove the canceled units.

$v = 1.30 \frac{km}{s} \frac{2.00 \cdot 10^{3}}{1} + 2.00 \frac{km}{s}$

Step 3.1.2.2

Divide using scientific notation.

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Step 3.1.2.2.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$v = 1.30 \frac{km}{s} ((\frac{2.00}{1}) (\frac{10^{3}}{1})) + 2.00 \frac{km}{s}$

Step 3.1.2.2.2

Divide $2.00$ by $1$ .

$v = 1.30 \frac{km}{s} (2.00 \frac{10^{3}}{1}) + 2.00 \frac{km}{s}$

Step 3.1.2.2.3

Divide $10^{3}$ by $1$ .

$v = 1.30 \frac{km}{s} \cdot 2.00 \cdot 10^{3} + 2.00 \frac{km}{s}$

Step 3.1.2.3

Combine fractions.

$v = 2.6000 \cdot 10^{3} \frac{km}{s} + 2.00 \frac{km}{s}$

Step 3.1.2.4

Convert $2.6000 \cdot 10^{3}$ to decimal.

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Step 3.1.2.4.1

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

$v = 2.6000 \cdot 1000 \frac{km}{s} + 2.00 \frac{km}{s}$

Step 3.1.2.4.2

Multiply $2.6000$ by $1000$ .

$v = 2600.0000 \frac{km}{s} + 2.00 \frac{km}{s}$

Step 3.2

Add $2600.0000 \frac{km}{s}$ and $2.00 \frac{km}{s}$ .

$v = 2602.0000 \frac{km}{s}$

Step 4

Round to $3$ significant figures.

$v = 2.60 \cdot 10^{3} \frac{km}{s}$

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