Physics Examples

$x = x_{0} + v_{0} \cdot t + \frac{1}{2} a t^{2}$

$x$	$=$	$?$
$x_{0}$	$=$	$0 m$
$v_{0}$	$=$	$1 \frac{m}{s}$
$t$	$=$	$3 s$
$a$	$=$	$- 9.8 \frac{m}{s^{2}}$

Step 1

Substitute the given values into $x = x_{0} + v_{0} \cdot t + \frac{1}{2} a t^{2}$ .

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Step 1.1

Substitute $0 m$ for $x_{0}$ .

$x = 0 m + v_{0} \cdot t + \frac{1}{2} a t^{2}$

Step 1.2

Substitute $1 \frac{m}{s}$ for $v_{0}$ .

$x = 0 m + 1 \frac{m}{s} \cdot t + \frac{1}{2} a t^{2}$

Step 1.3

Substitute $3 s$ for $t$ .

$x = 0 m + 1 \frac{m}{s} \cdot 3.0 s + \frac{1}{2} a {(3.0 s)}^{2}$

Step 1.4

Substitute $- 9.8 \frac{m}{s^{2}}$ for $a$ .

$x = 0 m + 1 \frac{m}{s} \cdot 3.0 s + \frac{1}{2} (- 9.8 \frac{m}{s^{2}}) {(3.0 s)}^{2}$

$x = 0 m + 1.0 \frac{m}{s} \cdot 3.0 s + \frac{1}{2} (- 9.8 \frac{m}{s^{2}}) {(3.0 s)}^{2}$

Step 2

Simplify the right side.

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Step 2.1

Simplify each term.

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Step 2.1.1

Cross cancel units.

$x = 0 m + 1.0 \frac{m}{s} \cdot \frac{3.0 s}{1} + \frac{1}{2} (- 9.8 \frac{m}{s^{2}}) {(3.0 s)}^{2}$

Step 2.1.2

Simplify the expression.

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Step 2.1.2.1

Remove the canceled units.

$x = 0 m + 1.0 \frac{m}{1} \cdot \frac{3.0}{1} + \frac{1}{2} (- 9.8 \frac{m}{s^{2}}) {(3.0 s)}^{2}$

Step 2.1.2.2

Combine fractions.

$x = 0 m + 3.0 m + \frac{1}{2} (- 9.8 \frac{m}{s^{2}}) {(3.0 s)}^{2}$

Step 2.1.3

Combine fractions.

$x = 0 m + 3.0 m + \frac{{(3.0 s)}^{2} \cdot - 9.8}{2} \frac{m}{s^{2}}$

Step 2.1.4

Simplify the numerator.

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Step 2.1.4.1

Apply the product rule to $3.0 s$ .

$x = 0 m + 3.0 m + \frac{{3.0}^{2} s^{2} \cdot - 9.8}{2} \frac{m}{s^{2}}$

Step 2.1.4.2

Multiply $- 9.8$ by ${3.0}^{2}$ .

$x = 0 m + 3.0 m + \frac{- 88.2 s^{2}}{2} \frac{m}{s^{2}}$

Step 2.1.5

Cross cancel units.

$x = 0 m + 3.0 m + \frac{- 88.2 s^{2}}{2} \frac{m}{s^{2}}$

Step 2.1.6

Remove the canceled units.

$x = 0 m + 3.0 m + \frac{- 88.2}{2} \cdot \frac{m}{1}$

Step 2.1.7

Combine fractions.

$x = 0 m + 3.0 m + \frac{- 88.2}{2} m$

Step 2.1.8

Divide $- 88.2$ by $2$ .

$x = 0 m + 3.0 m - 44.1 m$

Step 2.2

Add $0 m$ and $3.0 m$ .

$x = 3.0 m - 44.1 m$

Step 2.3

Subtract $44.1 m$ from $3.0 m$ .

$x = - 41.1 m$

Step 3

Round to $2$ significant figures.

$x = - 41 m$

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