Vertical position equation given gravity, initial vertical velocity, time, and height, s_y = -(1/2) g t^2 + v0y t + s_y0. Which form is correct?

Vertical position equation given gravity, initial vertical velocity, time, and height, s_y = -(1/2) g t^2 + v0y t + s_y0. Which form is correct?

• A. s_y = -(1/2) g t^2 + v0y t + s_y0
• B. s_y = (1/2) g t^2 + v0y t + s_y0
• C. s_y = g t^2 + v0y t + s_y0
• D. s_y = -(1/2) g t^2 - v0y t - s_y0

Answer: (A)

Constant vertical acceleration motion uses the form s_y(t) = s_y0 + v0y t + (1/2) a_y t^2. With upward chosen as positive, gravity gives a_y = -g, so s_y(t) = s_y0 + v0y t - (1/2) g t^2. This is exactly the given expression, just written with the terms in a different order. The s_y0 term sets the starting height, v0y t adds the displacement from the initial vertical velocity, and the - (1/2) g t^2 term accounts for the downward pull of gravity over time. The other forms would imply gravity acting upward or sign-flipped initial conditions, which don’t describe the standard downward acceleration under gravity.

Constant vertical acceleration motion uses the form s_y(t) = s_y0 + v0y t + (1/2) a_y t^2. With upward chosen as positive, gravity gives a_y = -g, so s_y(t) = s_y0 + v0y t - (1/2) g t^2. This is exactly the given expression, just written with the terms in a different order. The s_y0 term sets the starting height, v0y t adds the displacement from the initial vertical velocity, and the - (1/2) g t^2 term accounts for the downward pull of gravity over time. The other forms would imply gravity acting upward or sign-flipped initial conditions, which don’t describe the standard downward acceleration under gravity.