Horizontal velocity in the absence of horizontal acceleration?

Horizontal velocity in the absence of horizontal acceleration?

• A. v_x = v0x
• B. v_x = a_x t
• C. v_x = 0
• D. v_x = v0x t

Answer: (A)

When there is no horizontal acceleration, the horizontal component of velocity stays constant. The kinematic relation v_x = v0x + a_x t shows this: if a_x = 0, then v_x = v0x for all times. So the horizontal speed remains the initial horizontal speed, independent of how long you wait. This is why, in projectile motion without air resistance, the horizontal velocity doesn’t change while gravity alters only the vertical velocity. The other expressions would imply a change in horizontal velocity or zero velocity unless you specify a different starting condition, which isn’t given here.

When there is no horizontal acceleration, the horizontal component of velocity stays constant. The kinematic relation v_x = v0x + a_x t shows this: if a_x = 0, then v_x = v0x for all times. So the horizontal speed remains the initial horizontal speed, independent of how long you wait. This is why, in projectile motion without air resistance, the horizontal velocity doesn’t change while gravity alters only the vertical velocity. The other expressions would imply a change in horizontal velocity or zero velocity unless you specify a different starting condition, which isn’t given here.