413. A body with a mass of 8 kg moves in a straight line according to the law $s=$ $=2 t^{2}+3 t-1$. Find the kinetic energy of the body $\left(m v^{2} / 2\right)$ 3 seconds after the start of the motion.
Solution. Let's find the velocity of the body at any moment of time $t$:

$$
v=\frac{d s}{d t}=4 t+3
$$

Calculate the velocity of the body at the moment $t=3$:

$$
v_{t=3}=4 \cdot 3+3=15(\mathrm{M} / \mathrm{c})
$$

Determine the kinetic energy of the body at the moment $t=3$:

$$
\frac{m v^{2}}{2}=\frac{8 \cdot 15^{2}}{2}=900(\text { J })
$$