7. how much energy is dissipated (lost) if a car with a mass of 800 - kg car slows down from 40 m/s to 30 m/s?

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $K = \frac{1}{2}mv^{2}$, where $m$ is the mass and $v$ is the velocity.

Step2: Calculate initial kinetic energy

Given $m = 800\ kg$ and $v_1=40\ m/s$, the initial kinetic energy $K_1=\frac{1}{2}mv_1^{2}=\frac{1}{2}\times800\times40^{2}=160000\ J$.

Step3: Calculate final kinetic energy

Given $m = 800\ kg$ and $v_2 = 30\ m/s$, the final kinetic energy $K_2=\frac{1}{2}mv_2^{2}=\frac{1}{2}\times800\times30^{2}=360000\ J$.

Step4: Calculate energy dissipated

The energy dissipated $\Delta K=K_1 - K_2$. Substitute the values of $K_1$ and $K_2$: $\Delta K=160000 - 360000=140000\ J$.

Answer:

$140000\ J$