Motion and Newton's Laws

This is the densest physics topic in General Science and the one most worth learning properly, because it also underpins about half of Mechanical Comprehension.

Speed, velocity and acceleration

Speed is how fast something moves: distance over time. It has size only.

Velocity is speed with a direction. 30 miles per hour is a speed; 30 miles per hour north is a velocity.

Acceleration is the rate at which velocity changes: change in velocity over time.

Because velocity includes direction, changing direction is acceleration even at constant speed. A car rounding a bend at a steady 30 is accelerating, and so is anything moving in a circle. That is the question this distinction exists to support.

Deceleration is acceleration too, just negative.

Scalar quantities have size only: speed, distance, mass, time, energy. Vector quantities have size and direction: velocity, acceleration, force, momentum, displacement.

Distance against displacement is the same distinction applied to position. Walk 400 meters around a track and back to the start: distance 400, displacement zero.

Newton's three laws

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First law: inertia

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by an unbalanced force.

The key phrase is unbalanced force. Balanced forces produce no change. A book on a table has gravity pulling down and the table pushing up, and it stays put because they cancel.

Inertia is an object's resistance to a change in its motion, and it depends on mass. A loaded truck is harder to start and harder to stop than an empty one.

Everyday cases the test uses: a passenger thrown forward when a car brakes - they were moving and continued to; dishes staying put when a tablecloth is pulled quickly.

Second law: F = ma

Force equals mass times acceleration.

Rearranged: a = F / m. For the same force, more mass gives less acceleration.

A 4 kg object accelerates at 3 m/s per second. What force is acting?

4 times 3 is 12 newtons.

A 20 N force acts on a 5 kg object. What is the acceleration?

20 divided by 5 is 4 m/s per second.

This is the only formula in the topic and most calculations use it. Know which of the three quantities you are being asked for and rearrange.

Third law: action and reaction

For every action there is an equal and opposite reaction.

The forces act on two different objects, and that is the subtle part. When you push on a wall, you push the wall and the wall pushes you. Those are not the same object, so they do not cancel.

If they acted on the same object nothing could ever accelerate, which is the reasoning that makes the rule stick.

Examples: a rocket pushes exhaust down and the exhaust pushes the rocket up; a swimmer pushes water back and the water pushes the swimmer forward; a gun pushes the bullet forward and the bullet pushes the gun back as recoil.

Things in flight

A thrown or launched object follows a curved path called a parabola. Its sideways speed stays constant while gravity steadily pulls it down, and the two together trace the curve. That is why a ball dropped and a ball thrown sideways from the same height hit the ground at the same time: gravity acts on both the same way, and the sideways motion does not slow the fall.

Mass and weight

The distinction the subtest asks about more than anything else here.

On the Moon, gravity is about one sixth of Earth's. An astronaut's mass is unchanged and their weight is one sixth.

Weight = mass x gravitational acceleration. On Earth, g is about 9.8 m/s per second, so a 10 kg mass weighs about 98 newtons.

In free fall, all objects accelerate at the same rate regardless of mass, ignoring air resistance. A feather and a hammer dropped in a vacuum land together. A heavier object experiences more gravitational force and has proportionally more inertia to overcome, so the two effects cancel exactly - which is why this surprising fact is actually a consequence of F = ma.

Friction and gravity

Friction opposes motion between surfaces in contact. It is what stops things and what lets you walk, and it converts kinetic energy to heat.

Gravity is a force of attraction between any two masses. It grows with mass and falls off rapidly with distance.

Without friction and gravity, the first law would be obvious, because everything set moving would keep moving. Those two forces are why it does not look that way in daily life, which is why inertia took so long to be recognized.

What you can skip

Across all 2,104 General Science questions in our bank:

• Free-body diagrams, torque and kinematics equations never appear. The calculations asked are speed = distance / time, acceleration from a change in speed, and F = ma.
• Terminal velocity never appears by name.
• Vector arithmetic. Knowing that velocity has a direction and speed does not is enough; one question uses the word "vector".

Where people lose points

Giving weight in kilograms. Kilograms are mass; newtons are weight.

Saying mass changes on the Moon.

Saying something moving at constant speed around a curve is not accelerating.

Thinking action and reaction cancel. They act on different objects.

Confusing distance with displacement.

Saying heavier objects fall faster. Not in the absence of air resistance.

Work one in under a minute

A 1,200 kg car accelerates from rest to 20 m/s in 8 seconds. What force did the engine supply?

Acceleration first: change in velocity over time is 20 divided by 8, which is 2.5 m/s per second.

Force: 1,200 times 2.5 is 3,000 newtons.

Two steps, both from the table, and the order matters - you cannot use F = ma until you have a.

Where this leads

F = ma is the formula behind most of Mechanical Comprehension, and the energy transfers it produces are the next lesson.