The projectile

The projectile leaves the 10 m long barrel at an instantaneous speed of 500 m/s. What is the acceleration of the movement of the projectile in the barrel, and at what time will the projectile pass the barrel if we assume that It evenly accelerated the motion?

Correct answer:

a =  12500 m/s²

Step-by-step explanation:

$$\begin{gathered} s=10\text{m} \\ v=500\text{m/s} \\ v=a\cdot t \\ s=\frac{1}{2}\cdot a\cdot t^2 \\ s=\frac{1}{2}\cdot a\cdot (v/a{)}^2 \\ s=\frac{1}{2}\cdot v^2/a \\ a=\frac{v^2}{2\cdot s}=\frac{500^2}{2\cdot 10}=12500=12500{\text{m/s}}^2 \\ SK \\ t=v/a=500/12500=\frac{1}{25}=0.04\text{s} \\ {s}_2=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot 12500\cdot {\frac{1}{25}}^2=10\text{m} \\ {s}_2=s \end{gathered}$$

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