Physics Examples

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

$a_{c}$	$=$	$?$
$v$	$=$	$20 \frac{m}{s}$
$r$	$=$	$405 m$

Step 1

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

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Step 1.1

Substitute $20 \frac{m}{s}$ for $v$ .

$a_{c} = \frac{{(20 \frac{m}{s})}^{2}}{r}$

Step 1.2

Substitute $405 m$ for $r$ .

$a_{c} = \frac{{(20 \frac{m}{s})}^{2}}{405 m}$

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 $20 \frac{m}{s}$ .

$a_{c} = \frac{20^{2} {(\frac{m}{s})}^{2}}{405 m}$

Step 2.1.2

Raise $20$ to the power of $2$ .

$a_{c} = \frac{400 {(\frac{m}{s})}^{2}}{405 m}$

Step 2.1.3

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

$a_{c} = \frac{400 \frac{m^{2}}{s^{2}}}{405 m}$

Step 2.2

Cancel the common factor of $400$ and $405$ .

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Step 2.2.1

Factor $5$ out of $400 \frac{m^{2}}{s^{2}}$ .

$a_{c} = \frac{5 (80 \frac{m^{2}}{s^{2}})}{405 m}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $5$ out of $405 m$ .

$a_{c} = \frac{5 (80 \frac{m^{2}}{s^{2}})}{5 (81 m)}$

Step 2.2.2.2

Cancel the common factor.

$a_{c} = \frac{5 (80 \frac{m^{2}}{s^{2}})}{5 (81 m)}$

Step 2.2.2.3

Rewrite the expression.

$a_{c} = \frac{80 \frac{m^{2}}{s^{2}}}{81 m}$

Step 2.3

Factor $\frac{m^{2}}{s^{2}}$ out of $\frac{80 \frac{m^{2}}{s^{2}}}{81 m}$ .

$a_{c} = \frac{m^{2}}{s^{2}} \cdot \frac{80}{81 m}$

Step 2.4

Cross cancel units.

$a_{c} = \frac{m^{2}}{s^{2}} \cdot \frac{80}{81 m}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Remove the canceled units.

$a_{c} = \frac{m}{s^{2}} \cdot \frac{80}{81}$

Step 2.5.2

Combine fractions.

$a_{c} = \frac{80}{81} \frac{m}{s^{2}}$

Step 2.5.3

Divide $80$ by $81$ .

$a_{c} = 0.98765432 \frac{m}{s^{2}}$

Step 3

Round to $1$ significant figure.

$a_{c} = 1 \frac{m}{s^{2}}$

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