# If a spring has a constant of 7 (kg)/s^2, how much work will it take to extend the spring by 29 cm ?

$W = {\int}_{0}^{29} k x \mathrm{dx} = | \frac{1}{2} k {x}^{2} {|}_{0}^{29} = \frac{1}{2} 7 \times 29$
Work, $W = \int {\vec{F}}_{x} \cdot \vec{\mathrm{dx}} = \int F \mathrm{dx}$
Now for spring the Force $F = k x$ where k is spring constant
thus $W = \int k x \mathrm{dx}$
$W = {\int}_{0}^{29} k x \mathrm{dx} = | \frac{1}{2} k {x}^{2} {|}_{0}^{29} = \frac{1}{2} 7 \times 29$