A body of mass $$(5 \pm 0.5)$$ kg is moving with a velocity of $$(20 \pm 0.4)$$ m s$$^{-1}$$. Its kinetic energy will be

The kinetic energy is given by $$K = \frac{1}{2}mv^2$$.

$$K = \frac{1}{2} \times 5 \times (20)^2 = \frac{1}{2} \times 5 \times 400 = 1000 \text{ J}$$

For error calculation, we use the formula for relative error in kinetic energy:

$$\frac{\Delta K}{K} = \frac{\Delta m}{m} + 2\frac{\Delta v}{v}$$

$$\frac{\Delta K}{K} = \frac{0.5}{5} + 2 \times \frac{0.4}{20}$$

$$\frac{\Delta K}{K} = 0.1 + 0.04 = 0.14$$

$$\Delta K = 0.14 \times 1000 = 140 \text{ J}$$

Therefore, kinetic energy = $$(1000 \pm 140)$$ J.