Physics Examples

$a_{c} = \frac{v^{2}}{r}$

$a_{c}$	$=$	$?$
$v$	$=$	$15 \frac{m}{s}$
$r$	$=$	$810 m$

Step 1

Substitute the given values into $a_{c} = \frac{v^{2}}{r}$ .

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Step 1.1

Substitute $15 \frac{m}{s}$ for $v$ .

$a_{c} = \frac{{(15 \frac{m}{s})}^{2}}{r}$

Step 1.2

Substitute $810 m$ for $r$ .

$a_{c} = \frac{{(15 \frac{m}{s})}^{2}}{810 m}$

Step 2

Simplify the right side.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Apply the product rule to $15 \frac{m}{s}$ .

$a_{c} = \frac{15^{2} {(\frac{m}{s})}^{2}}{810 m}$

Step 2.1.2

Raise $15$ to the power of $2$ .

$a_{c} = \frac{225 {(\frac{m}{s})}^{2}}{810 m}$

Step 2.1.3

Apply the product rule to $\frac{m}{s}$ .

$a_{c} = \frac{225 \frac{m^{2}}{s^{2}}}{810 m}$

Step 2.2

Cancel the common factor of $225$ and $810$ .

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Step 2.2.1

Factor $45$ out of $225 \frac{m^{2}}{s^{2}}$ .

$a_{c} = \frac{45 (5 \frac{m^{2}}{s^{2}})}{810 m}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $45$ out of $810 m$ .

$a_{c} = \frac{45 (5 \frac{m^{2}}{s^{2}})}{45 (18 m)}$

Step 2.2.2.2

Cancel the common factor.

$a_{c} = \frac{45 (5 \frac{m^{2}}{s^{2}})}{45 (18 m)}$

Step 2.2.2.3

Rewrite the expression.

$a_{c} = \frac{5 \frac{m^{2}}{s^{2}}}{18 m}$

Step 2.3

Factor $\frac{m^{2}}{s^{2}}$ out of $\frac{5 \frac{m^{2}}{s^{2}}}{18 m}$ .

$a_{c} = \frac{m^{2}}{s^{2}} \cdot \frac{5}{18 m}$

Step 2.4

Cross cancel units.

$a_{c} = \frac{m^{2}}{s^{2}} \cdot \frac{5}{18 m}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Remove the canceled units.

$a_{c} = \frac{m}{s^{2}} \cdot \frac{5}{18}$

Step 2.5.2

Combine fractions.

$a_{c} = \frac{5}{18} \frac{m}{s^{2}}$

Step 2.5.3

Divide $5$ by $18$ .

$a_{c} = 0.27777777 \frac{m}{s^{2}}$

Step 3

Round to $2$ significant figures.

$a_{c} = 0.28 \frac{m}{s^{2}}$

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