Linear motion: (i) acceleration g of free fall

The idea

Free fall means motion under gravity alone, with air resistance negligible. Near the Earth's surface the acceleration is g, approximately 9.81 m s⁻², directed downwards. Because g is constant, the equations of motion apply: for a dropped object starting from rest, v = gt and s = ½gt², so a fall of 4.9 m takes about 1.0 s. Note that g is an acceleration, not a force or a speed, and its unit is m s⁻². All objects fall with the same g in the absence of air resistance, which is why a feather and a coin match in a vacuum. In multiple-choice questions, check whether the object starts from rest, whether upward is taken as positive, and whether the value quoted is g or a multiple of it.

What earns the marks

• g is the acceleration of a body in free fall, equal to about 9.81 m s⁻² near the Earth's surface.
• g is directed vertically downwards and is treated as constant over the distances considered at this level.
• In the absence of air resistance, all bodies fall with the same acceleration g regardless of mass.
• For an object released from rest, v = gt and s = ½gt² follow directly from the equations of motion with a = g.

Common mistakes and how to put them right

• Confusing g with the gravitational force or weight.

  Put it right: g is an acceleration in m s⁻², whereas weight is a force in N.

• Believing heavier objects fall faster.

  Put it right: In the absence of air resistance all bodies have the same acceleration g.

• Using g = 9.81 m s⁻² with the wrong sign or direction.

  Put it right: Choose a positive direction and apply it consistently to displacement, velocity and acceleration.

Exam tips

• Check the unit in each option: an acceleration must be in m s⁻², so any answer in m s⁻¹ or N can be eliminated immediately.
• Decide your positive direction before substituting into an equation, and keep the sign of g consistent with it.
• For a dropped object, remember the initial velocity is zero, which simplifies v = gt and s = ½gt².