Which one of the following holds true for a freely falling object?

Correct — D, it moves with a uniform acceleration. Free fall is the case where gravity is the only force acting, air resistance being neglected. Near the Earth's surface the gravitational field strength is about 9.8 metres per second squared and barely changes over the heights an ordinary problem involves, and it is the same for every body regardless of mass — a heavier object feels a proportionately larger force on a proportionately larger mass, so the acceleration comes out identical. A constant force on a fixed mass gives a constant acceleration, so the falling body gains roughly 9.8 metres per second of speed in each successive second. That fixed rate of gain is the uniform acceleration; because the speed keeps growing, neither velocity nor speed can be uniform.

• (a)It moves with a uniform velocity. — Uniform velocity means no change in either magnitude or direction, which requires zero net force. A falling body has gravity acting on it throughout, so its velocity grows the whole way down.
• (b)It moves with a uniform speed. — This is the same error with direction stripped out. The magnitude of the velocity is precisely the quantity that increases second by second, so it is the last thing about free fall that stays constant.
• (c)It moves with a non-uniform acceleration. — The field strength does fall off with height and does vary a little with latitude, but over the drop distances of a school or exam problem that variation is negligible. Acceleration turns genuinely non-uniform only once air resistance is admitted — and a body slowed by the air towards terminal velocity is no longer in free fall.

Three equations of motion follow once the acceleration is constant: the velocity after time t is u + gt, the distance fallen is ut + half of g t squared, and the velocity satisfies v squared equals u squared plus 2gs. Dropped from rest, a body is moving at about 9.8 metres per second after one second, 19.6 after two and 29.4 after three, while the distances fallen in those successive seconds go 4.9 m, 14.7 m and 24.5 m — the speeds grow in an arithmetic run and the total distance grows with the square of the time.

The everyday intuition that heavier things fall faster comes from air resistance, not from gravity, and separating the two is the real content of this question. Galileo argued the point; the cleanest demonstration was on the Moon in 1971, when the Apollo 15 commander David Scott released a hammer and a falcon feather together in a vacuum and they struck the surface at the same instant. The distinction also explains why option (c) is not simply silly — a real parachutist genuinely does accelerate less and less until the drag matches the weight and the acceleration reaches zero at terminal velocity. That motion is not free fall, which is exactly the boundary the examiner is probing.

• Acceleration in free fall near the Earth's surface is about 9.8 metres per second squared and is independent of the falling body's mass.
• Velocity and speed both grow continuously during free fall, while acceleration stays fixed.
• Distance fallen from rest grows with the square of the time, so the second second covers three times the first second's distance.
• Gravitational field strength is GM divided by the square of the distance from the centre, so it decreases with altitude and is slightly larger at the poles than at the equator.
• Once air resistance is included the body approaches terminal velocity, at which the net force and the acceleration are zero.

• Assuming a heavier body falls faster, which is an air-resistance effect and not a gravitational one.
• Reading increasing speed as increasing acceleration.
• Applying the constant-acceleration equations to a body that has already reached terminal velocity.

Asked as a single-property recall item where the three wrong options are all statements that would be true of some other kind of motion.

• practice — not a real PYQ

  A stone is dropped from rest and takes 3 seconds to reach the ground. Taking g as 10 metres per second squared and ignoring air resistance, the height from which it was dropped is

  • (a)30 m
  • (b)45 m
  • (c)60 m
  • (d)90 m

  Answer(b) 45 m — with u = 0 the distance is half of g t squared, which is 0.5 × 10 × 9 = 45 metres.

• practice — not a real PYQ

  A body falling through air has reached its terminal velocity. Its acceleration at that moment is

  • (a)equal to g
  • (b)greater than g
  • (c)zero
  • (d)directed upward and equal to g

  Answer(c) zero — terminal velocity is reached when the upward drag exactly balances the weight, leaving no net force and therefore no acceleration.