Physics Examples

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

$\overline{a}$	$=$	$- 0.6 \frac{m}{s^{2}}$
$v$	$=$	$?$
$v_{0}$	$=$	$25 \frac{m}{s}$
$t$	$=$	$10 s$

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 $- 0.6 \frac{m}{s^{2}}$ for $\overline{a}$ .

$v = - 0.6 \frac{m}{s^{2}} t + v_{0}$

Step 2.2

Substitute $25 \frac{m}{s}$ for $v_{0}$ .

$v = - 0.6 \frac{m}{s^{2}} t + 25 \frac{m}{s}$

Step 2.3

Substitute $10 s$ for $t$ .

$v = - 0.6 \frac{m}{s^{2}} (10 s) + 25 \frac{m}{s}$

$v = - 0.600 \frac{m}{s^{2}} (10.0 s) + 25.0 \frac{m}{s}$

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.

$v = - 0.600 \frac{m}{s^{2}} \frac{10.0 s}{1} + 25.0 \frac{m}{s}$

Step 3.1.2

Simplify the expression.

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Step 3.1.2.1

Remove the canceled units.

$v = - 0.600 \frac{m}{s} \frac{10.0}{1} + 25.0 \frac{m}{s}$

Step 3.1.2.2

Combine fractions.

$v = - 6.0000 \frac{m}{s} + 25.0 \frac{m}{s}$

Step 3.2

Add $- 6.0000 \frac{m}{s}$ and $25.0 \frac{m}{s}$ .

$v = 19.0000 \frac{m}{s}$

Step 4

Round to $3$ significant figures.

$v = 19.0 \frac{m}{s}$

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