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How do objects move when gravity is the only force acting, and why do a heavy and a light object fall together?

Analyze free fall as motion with constant acceleration g, using the kinematic equations to find fall time, speed, or height, and explain why mass does not affect the rate of fall (MA STE Introductory Physics, Motion and Forces).

A standard-level answer on free fall for the Massachusetts High School Introductory Physics MCAS: gravity as a constant acceleration, using the kinematic equations for falling objects, and why all objects fall at the same rate when air resistance is ignored.

Generated by Claude Opus 4.812 min answer

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  1. What this topic is asking
  2. Free fall as constant acceleration
  3. Why mass does not matter
  4. Going up as well as down
  5. Try this

What this topic is asking

Free fall is the simplest example of accelerated motion, and the Massachusetts Introductory Physics MCAS uses it to test the kinematic equations and a deep conceptual point. You must analyze an object falling under gravity as constant-acceleration motion with a=ga = g, calculate the fall time, landing speed, or height, and explain why a heavy and a light object fall together when air resistance is ignored. This links kinematics to the idea of cause and effect: gravity is the cause, the acceleration gg is the effect.

Free fall as constant acceleration

Because the acceleration is constant, free fall is just the kinematic equations with a=ga = g pointing downward. The most common case is an object dropped from rest, so the initial velocity vi=0v_i = 0 and the equations simplify:

vf=gtandd=12gt2v_f = gt \qquad \text{and} \qquad d = \tfrac{1}{2}gt^2

So after 11 s a dropped object is moving at 1010 m/s and has fallen 55 m; after 22 s it is moving at 2020 m/s and has fallen 2020 m. The speed grows in proportion to time, and the distance grows with time squared.

Why mass does not matter

This is the conceptual point the MCAS loves, because intuition says heavy things fall faster. The resolution comes from Newton's second law. The force pulling an object down is its weight, Fg=mgF_g = mg. Its acceleration is force divided by mass:

a=Fgm=mgm=ga = \frac{F_g}{m} = \frac{mg}{m} = g

The mass cancels. A heavy object has a larger weight (a larger downward force), but it also has more mass to move, and the two effects exactly offset. So every object, heavy or light, accelerates at the same gg and falls at the same rate, as long as air resistance is negligible. The famous demonstration is a feather and a coin (or a hammer) released together in a vacuum: they land at the same instant.

In real air, light objects with a large surface area (a feather, a sheet of paper) fall slower, but that is air resistance, not gravity. Remove the air and they fall together.

Going up as well as down

Free fall also covers objects thrown upward. On the way up, gravity still acts downward, so the object decelerates at gg, stops momentarily at the top (where v=0v = 0), then accelerates downward. If you call up positive, the acceleration is −g-g throughout, even at the top. A ball thrown up at 2020 m/s takes 2.02.0 s to reach the top (since 0=20−10t0 = 20 - 10t), then 2.02.0 s to fall back, returning at 2020 m/s.

Try this

Q1. An object is dropped from rest. How fast is it moving after 4.04.0 s? (Take g=10g = 10 m/s squared.) [2]

  • Cue. vf=gt=(10)(4.0)=40v_f = gt = (10)(4.0) = 40 m/s.

Q2. Explain why a hammer and a feather hit the ground together on the Moon. [2]

  • Cue. The Moon has no atmosphere, so there is no air resistance; gravity is the only force, and all objects fall with the same acceleration regardless of mass.

Exam-style practice questions

Practice questions written in the style of MA DESE exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

MA Physics MCAS (style)3 marksA ball is dropped from rest from the top of a building and takes 2.02.0 s to reach the ground. Take g=10g = 10 m/s squared and ignore air resistance. (a) Calculate the speed of the ball just before it lands. (b) Calculate the height of the building.
Show worked answer →

A 3-point item applying the kinematic equations to free fall.

(a) Speed (1 point): use vf=vi+atv_f = v_i + at with vi=0v_i = 0 and a=g=10a = g = 10 m/s squared. vf=0+(10)(2.0)=20v_f = 0 + (10)(2.0) = 20 m/s.
(b) Height (up to 2 points): use d=vit+12at2=0+12(10)(2.0)2=12(10)(4.0)=20d = v_i t + \tfrac{1}{2}at^2 = 0 + \tfrac{1}{2}(10)(2.0)^2 = \tfrac{1}{2}(10)(4.0) = 20 m.

Markers reward using gg as the acceleration and vi=0v_i = 0 for "dropped from rest." The height is 2020 m.

MA Physics MCAS (style)2 marksIn a vacuum tube, a feather and a coin are released at the same instant from the same height. (a) State which one lands first. (b) Explain your answer in terms of the force of gravity and acceleration.
Show worked answer →

A 2-point conceptual item on why mass does not change the rate of free fall.

(a) 1 point: they land at the same time (together).
(b) 1 point: in a vacuum there is no air resistance, so gravity is the only force. Although the coin has a larger weight, it also has more mass, and acceleration is force divided by mass, so the larger force and larger mass cancel to give the same acceleration gg for both. Markers reward the idea that all objects fall with the same acceleration when air resistance is removed.

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