# Problem № 6 (15 points)

A body is thrown vertically upwards from a balcony. The dependence of the modulus of the body's acceleration on time is shown in the graph. Using this dependence, estimate the initial speed of the body. The acceleration due to gravity $g=10 \mathrm{~m} / \mathrm{s}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_dde97d69ac546735bb46g-03.jpg?height=1057&width=1490&top_left_y=531&top_left_x=340)

Answer: $30 \mathrm{~m} / \mathrm{s}$

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# Solution and evaluation criteria:

The graph looks this way due to the presence of air resistance acting on the ball.

(4 points)

At time $t=2 s$, the acceleration equals the acceleration due to gravity. Therefore, at this moment, the ball was at the highest point of its trajectory and its velocity $v=0 m/s$. (4 points)

The change in velocity equals the area under the graph

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