Physics Examples

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

Step 1

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

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

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

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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Simplify the numerator.

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

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

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

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

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

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

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

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

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

Cancel the common factors.

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Factor $45$ out of $810 m$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cross cancel units.

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

Simplify the expression.

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Remove the canceled units.

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

Combine fractions.

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

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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