Which statement is true for horizontal motion with zero horizontal acceleration?

Which statement is true for horizontal motion with zero horizontal acceleration?

• A. Horizontal velocity remains constant
• B. Horizontal position remains fixed
• C. Vertical velocity remains zero
• D. Gravity affects horizontal motion but not vertical

Answer: (A)

When horizontal acceleration is zero, the horizontal part of the motion is uniform. The net force in that direction is zero, so dv_x/dt = 0 and the horizontal velocity stays the same as time passes. That means the horizontal position changes linearly with time: x(t) = x0 + v_x0 t, so it won’t stay fixed unless the initial horizontal velocity is zero. Vertical motion, on the other hand, is governed by gravity, which provides downward acceleration, so the vertical velocity changes with time regardless of the horizontal motion. So gravity affects vertical motion, not horizontal. The statement that the horizontal velocity remains constant is the true one.

When horizontal acceleration is zero, the horizontal part of the motion is uniform. The net force in that direction is zero, so dv_x/dt = 0 and the horizontal velocity stays the same as time passes. That means the horizontal position changes linearly with time: x(t) = x0 + v_x0 t, so it won’t stay fixed unless the initial horizontal velocity is zero. Vertical motion, on the other hand, is governed by gravity, which provides downward acceleration, so the vertical velocity changes with time regardless of the horizontal motion. So gravity affects vertical motion, not horizontal. The statement that the horizontal velocity remains constant is the true one.