Physics Examples

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

$\overline{a}$	$=$	$2 \frac{m}{s^{2}}$
$v$	$=$	$?$
$v_{0}$	$=$	$5 \frac{m}{s}$
$t$	$=$	$7.3 s$

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

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

$\overline{a}$ .

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

Step 2.2

Substitute

$5 \frac{m}{s}$ for

$v_{0}$ .

$v = 2 \frac{m}{s^{2}} t + 5 \frac{m}{s}$

Step 2.3

Substitute

$7.3 s$ for

$t$ .

$v = 2 \frac{m}{s^{2}} (7.3 s) + 5 \frac{m}{s}$

$v = 2.00 \frac{m}{s^{2}} (7.30 s) + 5.00 \frac{m}{s}$

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.

$v = 2.00 \frac{m}{s^{2}} \frac{7.30 s}{1} + 5.00 \frac{m}{s}$

Step 3.1.2

Simplify the expression.

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Step 3.1.2.1

Remove the canceled units.

$v = 2.00 \frac{m}{s} \frac{7.30}{1} + 5.00 \frac{m}{s}$

Step 3.1.2.2

Combine fractions.

$v = 14.6000 \frac{m}{s} + 5.00 \frac{m}{s}$

Step 3.2

Add

$14.6000 \frac{m}{s}$ and

$5.00 \frac{m}{s}$ .

$v = 19.6000 \frac{m}{s}$

Step 4

Round to

$3$ significant figures.

$v = 19.6 \frac{m}{s}$

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