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| <h3 id="back-link"><a href="../../#1.2">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.2">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $1.2.6.$ The graph of the velocity of the body versus time looks like a semicircle. Maximum velocity of the body $v_0$, time of motion $t_0$. Determine the distance traveled by the body. | | $1.2.6.$ The graph of the velocity of the body versus time looks like a semicircle. Maximum velocity of the body $v_0$, time of motion $t_0$. Determine the distance traveled by the body. |
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| For problem $1.2.6$ | | For problem $1.2.6$ |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| The traveled path can be found as the area under the graph $v(t)$. If the area of the semicircle $S=\pi r^2/2$, then the required path: | | The traveled path can be found as the area under the graph $v(t)$. If the area of the semicircle $S=\pi r^2/2$, then the required path: |
| | | |
| $$ | | $$ |
| x = \frac{\pi v_0t_0}{4} | | x = \frac{\pi v_0t_0}{4} |
| $$ | | $$ |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
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| $$x = (\pi /4)v_0t_0$$ | | $$x = (\pi /4)v_0t_0$$ |
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