Physics Examples

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

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

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

Step 1

Substitute the given values into

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

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

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Step 1.1

Substitute

0 m

$0 m$ for

x_{0}

$x_{0}$ .

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

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

Step 1.2

Substitute

1 \frac{m}{s}

$1 \frac{m}{s}$ for

v_{0}

$v_{0}$ .

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

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

Step 1.3

Substitute

3 s

$3 s$ for

t

$t$ .

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

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

Step 1.4

Substitute

- 9.8 \frac{m}{s^{2}}

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

a

$a$ .

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

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

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}

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

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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