At time t = 0, what is s_y in the vertical position equation?

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Multiple Choice

At time t = 0, what is s_y in the vertical position equation?

Explanation:
The main idea is that at the starting moment, the vertical position equals its initial value. In the vertical motion equation s_y(t) = s_y0 + v0y t + (1/2) a_y t^2, plug in t = 0: s_y(0) = s_y0 + v0y(0) + (1/2) a_y (0)^2 = s_y0. So the vertical position at time zero is s_y0, the initial vertical position. The other options don’t fit because v0y is the initial vertical velocity, not a position; -s_y0 would be the negative of the initial position, which isn’t what the equation yields at t = 0; and zero would only hold if the initial height is defined as zero, which is a special coordinate choice rather than the general definition.

The main idea is that at the starting moment, the vertical position equals its initial value. In the vertical motion equation s_y(t) = s_y0 + v0y t + (1/2) a_y t^2, plug in t = 0: s_y(0) = s_y0 + v0y(0) + (1/2) a_y (0)^2 = s_y0. So the vertical position at time zero is s_y0, the initial vertical position.

The other options don’t fit because v0y is the initial vertical velocity, not a position; -s_y0 would be the negative of the initial position, which isn’t what the equation yields at t = 0; and zero would only hold if the initial height is defined as zero, which is a special coordinate choice rather than the general definition.

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