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| <title>Draw a graph of coordinate versus time for a rectilinear motion that satisfies two conditions simultaneously: a. the average speed in the time interval from 2 to 6 s is 5 m/s; b. the maximum speed in the same interval is 15 m/s.</title> | | <title>Draw a graph of coordinate versus time for a rectilinear motion that satisfies two conditions simultaneously: a. the average speed in the time interval from 2 to 6 s is 5 m/s; b. the maximum speed in the same interval is 15 m/s.</title> |
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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> |
| $1.2.4.$ Draw a graph of coordinate versus time for a rectilinear motion that satisfies two conditions simultaneously: | | $1.2.4.$ Draw a graph of coordinate versus time for a rectilinear motion that satisfies two conditions simultaneously: |
| | | |
| a. the average speed in the time interval from $2$ to $6$ s is $5$ m/s; | | a. the average speed in the time interval from $2$ to $6$ s is $5$ m/s; |
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| b. the maximum speed in the same interval is $15$ m/s. | | b. the maximum speed in the same interval is $15$ m/s. |
| </p> | | </p> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| It is necessary to choose such a dependence so that the derivative of the coordinate in time, aka velocity, obeys the conditions of the problem. | | It is necessary to choose such a dependence so that the derivative of the coordinate in time, aka velocity, obeys the conditions of the problem. |
| </p> | | </p> |
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| An example of such a function is shown at the bottom: | | An example of such a function is shown at the bottom: |
| </p> | | </p> |
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| <p> | | <p> |
| The derivative of $x(t) = 2.5t^2-15t$ is equal to | | The derivative of $x(t) = 2.5t^2-15t$ is equal to |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $v(t) = 5t-15$ | | $v(t) = 5t-15$ |
| </p> | | </p> |
| <p> | | <p> |
| What satisfies the conditions of the problem. | | What satisfies the conditions of the problem. |
| </p> | | </p> |
| | | |
| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| Any graph with a coordinate change of $20$ m in the specified time and with the greatest “slope” of the tangent $15$ m/s | | Any graph with a coordinate change of $20$ m in the specified time and with the greatest “slope” of the tangent $15$ m/s |
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