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$$
\begin{array}{l}{\text { Determine the energy required to accelerate an } 800-\mathrm{kg}} \\ {\text { car from rest to } 100 \mathrm{km} / \mathrm{hon} \text { a level road }}\end{array}
$$

$$
m=800 \mathrm{kg}
$$

$$
V_{1}=0
$$

$$
V_{2}=100 \mathrm{km} / \mathrm{h} \longrightarrow
$$$$
\frac{1000}{3600}=2.778 \mathrm{m} / \mathrm{s}
$$

$$
w_{a}=\frac{1}{2} m\left(v_{2}^{2}-v_{1}^{2}\right)
$$

$$
=\frac{1}{2}(800)\left(2.778^{2}\right)*
$$$$
\frac{1kg}{1000 kg m^2/s^2}
$$

$$
={309 \mathrm{KJ}}
$$

$$
\begin{array}{l}{\text { How much work, in } \mathrm{kJ} \text { , can a spring whose spring constant }} \\ {\text { is } 3 \mathrm{kN} / \mathrm{cm} \text { produce after it has been compressed } 3 \mathrm{cm}} \\ {\text { from its unloaded length? }}\end{array}
$$

$$
W=\int_{1}^{2} F d s=\int_{1}^{2} k x d x
$$

$$
=k \int_{1}^{2} x d x
$$

$$
=\frac{k}{2}\left(x_{2}^{2}-x_{1}^{2}\right)
$$

$$
=\frac{300}{2}\left(0.03^{2}-0^{2}\right)=0.135 \mathrm{kN} \cdot \mathrm{m}
$$

$$
\frac{1kJ}{1{k N \cdot m}} \longrightarrow W=0.135 \mathrm{k}{J}
$$

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