In translational equilibrium, if the net force is zero, which statement is true about acceleration and velocity?

In translational equilibrium, if the net force is zero, which statement is true about acceleration and velocity?

• A. F_net = 0 implies a = 0 and v is constant
• B. F_net = 0 implies a increases with time
• C. F_net = 0 implies v must be zero
• D. F_net = 0 implies acceleration is varying

Answer: (A)

When the net force on a body is zero, the acceleration must be zero. This comes from Newton's first law: translational equilibrium means no net external force, so there is no change in motion. Since acceleration is the time rate of change of velocity, a = 0 implies dv/dt = 0, so the velocity does not change with time and stays constant. The velocity could be any constant value, including zero (the object could be at rest or moving at a constant speed in a straight line). The other ideas would require a nonzero or changing force, which contradicts equilibrium: zero acceleration does not mean velocity must be zero, and acceleration cannot be increasing or varying when there’s no net force.

When the net force on a body is zero, the acceleration must be zero. This comes from Newton's first law: translational equilibrium means no net external force, so there is no change in motion. Since acceleration is the time rate of change of velocity, a = 0 implies dv/dt = 0, so the velocity does not change with time and stays constant. The velocity could be any constant value, including zero (the object could be at rest or moving at a constant speed in a straight line).

The other ideas would require a nonzero or changing force, which contradicts equilibrium: zero acceleration does not mean velocity must be zero, and acceleration cannot be increasing or varying when there’s no net force.