Physics Examples

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

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

$x$ $x$	$=$ $=$	$?$ $?$
$x_{0}$ $x_{0}$	$=$ $=$	$0 m$ $0 m$
$v_{0}$ $v_{0}$	$=$ $=$	$0 \frac{m}{s}$ $0 \frac{m}{s}$
$t$ $t$	$=$ $=$	$5.5 s$ $5.5 s$
$a$ $a$	$=$ $=$	$6 \frac{m}{s^{2}}$ $6 \frac{m}{s^{2}}$

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

0 \frac{m}{s}

$0 \frac{m}{s}$ for

v_{0}

$v_{0}$ .

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

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

Step 1.3

Substitute

5.5 s

$5.5 s$ for

t

$t$ .

x = 0 m + 0 \frac{m}{s} \cdot 5.50 s + \frac{1}{2} a {(5.50 s)}^{2}

$x = 0 m + 0 \frac{m}{s} \cdot 5.50 s + \frac{1}{2} a {(5.50 s)}^{2}$

Step 1.4

Substitute

6 \frac{m}{s^{2}}

$6 \frac{m}{s^{2}}$ for

a

$a$ .

x = 0 m + 0 \frac{m}{s} \cdot 5.50 s + \frac{1}{2} (6 \frac{m}{s^{2}}) {(5.50 s)}^{2}

$x = 0 m + 0 \frac{m}{s} \cdot 5.50 s + \frac{1}{2} (6 \frac{m}{s^{2}}) {(5.50 s)}^{2}$

x = 0 m + 0 \frac{m}{s} \cdot 5.50 s + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}

$x = 0 m + 0 \frac{m}{s} \cdot 5.50 s + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}$

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 + 0 \frac{m}{s} \cdot \frac{5.50 s}{1} + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}

$x = 0 m + 0 \frac{m}{s} \cdot \frac{5.50 s}{1} + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}$

Step 2.1.2

Simplify the expression.

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Step 2.1.2.1

Remove the canceled units.

x = 0 m + 0 \frac{m}{1} \cdot \frac{5.50}{1} + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}

$x = 0 m + 0 \frac{m}{1} \cdot \frac{5.50}{1} + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}$

Step 2.1.2.2

Combine fractions.

x = 0 m + 0 m + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}

$x = 0 m + 0 m + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}$

x = 0 m + 0 m + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}

$x = 0 m + 0 m + \frac{1}{2} (6.00 \frac{m}{s^{2}}) {(5.50 s)}^{2}$

Step 2.1.3

Combine fractions.

x = 0 m + 0 m + \frac{{(5.50 s)}^{2} \cdot 6.00}{2} \frac{m}{s^{2}}

$x = 0 m + 0 m + \frac{{(5.50 s)}^{2} \cdot 6.00}{2} \frac{m}{s^{2}}$

Step 2.1.4

Simplify the numerator.

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Step 2.1.4.1

Apply the product rule to

5.50 s

$5.50 s$ .

x = 0 m + 0 m + \frac{{5.50}^{2} s^{2} \cdot 6.00}{2} \frac{m}{s^{2}}

$x = 0 m + 0 m + \frac{{5.50}^{2} s^{2} \cdot 6.00}{2} \frac{m}{s^{2}}$

Step 2.1.4.2

Multiply

6.00

$6.00$ by

{5.50}^{2}

${5.50}^{2}$ .

x = 0 m + 0 m + \frac{181.5000 s^{2}}{2} \frac{m}{s^{2}}

$x = 0 m + 0 m + \frac{181.5000 s^{2}}{2} \frac{m}{s^{2}}$

x = 0 m + 0 m + \frac{181.5000 s^{2}}{2} \frac{m}{s^{2}}

$x = 0 m + 0 m + \frac{181.5000 s^{2}}{2} \frac{m}{s^{2}}$

Step 2.1.5

Cross cancel units.

x = 0 m + 0 m + \frac{181.5000 s^{2}}{2} \frac{m}{s^{2}}

$x = 0 m + 0 m + \frac{181.5000 s^{2}}{2} \frac{m}{s^{2}}$

Step 2.1.6

Remove the canceled units.

x = 0 m + 0 m + \frac{181.5000}{2} \cdot \frac{m}{1}

$x = 0 m + 0 m + \frac{181.5000}{2} \cdot \frac{m}{1}$

Step 2.1.7

Combine fractions.

x = 0 m + 0 m + \frac{181.5000}{2} m

$x = 0 m + 0 m + \frac{181.5000}{2} m$

Step 2.1.8

Divide

181.5000

$181.5000$ by

2

$2$ .

x = 0 m + 0 m + 90.7500 m

$x = 0 m + 0 m + 90.7500 m$

x = 0 m + 0 m + 90.7500 m

$x = 0 m + 0 m + 90.7500 m$

Step 2.2

Add

0 m

$0 m$ and

0 m

$0 m$ .

x = 0 m + 90.7500 m

$x = 0 m + 90.7500 m$

Step 2.3

Add

0 m

$0 m$ and

90.7500 m

$90.7500 m$ .

x = 90.7500 m

$x = 90.7500 m$

x = 90.7500 m

$x = 90.7500 m$

Step 3

Round to

3

$3$ significant figures.

x = 90.8 m

$x = 90.8 m$

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