Answer Key: Newton's Laws and Transportation Safety

Full credit for any reasonable notice + wonder. Ideal: Notice — "riders move forward even though nothing pushed them." Wonder — "why do we go forward when the bus goes forward and then stops?" Accept any on-topic wonder. Science note (not required from students): the riders' bodies have inertia and tend to keep moving forward (Newton's First Law) while the bus is being slowed by braking friction.

Accept any two real features with a plausible purpose. Examples: seatbelt (holds you back / keeps you in the seat), airbag (cushions the head/chest), crumple zone (front of car folds to absorb the hit), headrest (stops the head snapping back). More than one answer is defensible.

Newton's First Law (the law of inertia). The property shown by the dashed arrow is inertia — the body's tendency to keep moving forward at its original speed until a net force (like the seatbelt) slows it. Watch for students calling inertia "a force" — it is not (see misconceptions).

a) O — a value read directly from the table (32 m).
b) I — it explains a cause ("because it spreads the stop over more time and area").
c) O — a value read directly from the table (2,700 N).
d) I — a reasoned conclusion about a consequence ("would be hurt worse").
Observation = measured/read directly; inference = a conclusion reasoned from evidence.

5a — First Law (inertia). The unbelted rider keeps moving forward because no net force acts on the body until something stops it.
5b — Second Law (F = ma). At the same braking force, more speed means the car must lose more motion, so it takes a longer distance/time to stop (accept reasoning that more speed → more distance for the same deceleration). Accept First Law reasoning only if a student clearly ties it to "more motion to change." Best answer is Second Law.
5c — Third Law (action–reaction). The belt pushes back on the rider and the rider pushes forward on the belt with an equal, opposite force on two different objects.

6a. F = m × a = 50 kg × 8 m/s² = 400 N. (Full credit for correct setup and 400 N; accept units written as newtons.)
6b. F = 80 kg × 8 m/s² = 640 N. The 80 kg dummy needs the larger force because it has more mass — for the same acceleration, more mass requires more force (F = ma). This is also more inertia to overcome. Common error: multiplying wrong or dropping units; a bare "640" with correct work still earns credit.

Award full credit if the student names a feature and explains that it lowers the peak force by spreading the stop over more time or more area, tied to a Newton's law. Worked examples:

• Seatbelt: stretches slightly and holds the rider back so the body slows with the car over more time instead of hitting the dash suddenly. More stopping time → smaller acceleration → smaller force (F = ma). Table 1 shows belted forces are far lower than unbelted.
• Crumple zone: the front of the car folds and collapses, extending the crash over more time so the car (and rider) decelerate more gradually — lower acceleration, lower force (F = ma).
• Airbag: inflates to catch the head/chest, spreading the force over a larger area and more time than a hard dashboard, lowering the peak force.
• Headrest: stops the head from snapping backward (inertia, First Law) during a rear impact, reducing the sudden force on the neck.

Any feature earns credit if the "more time / more area → less force" mechanism and a law are correct.

Model answer. Claim: The city should require lap-and-shoulder seatbelts on its school buses. Evidence: (1) In Table 1, the peak force on the 50 kg dummy at 20 m/s was 4,000 N with a seatbelt but 10,500 N without — the belt cut the force to well under half. (2) In Figure 1, the seatbelt applies a backward force on the rider so the body slows with the car instead of continuing forward by inertia. Reasoning: By Newton's First Law, an unbelted rider keeps moving forward in a sudden stop; the belt provides the net force that stops the body more gradually, and by F = ma a longer stopping time means a smaller acceleration and a smaller force on the rider.
Defensible alternates: A student may recommend crumple zones (extend crash time → lower acceleration → lower force, F = ma) or padded high seatbacks/headrests (catch the rider, spread force over more area/time). Accept any recommendation supported by two correct pieces of evidence and sound law-based reasoning. The seatbelt claim is strongest because Table 1 directly quantifies its effect.

Articulate: accept any accurate plain-language statement of one law (e.g., "things keep moving unless a force stops them" for the First Law).
Connect: the cited row/arrow must match the chosen law (e.g., inertia arrow → First Law; belted-vs-unbelted force column → Second Law, F = ma; the belt push/rider push pair → Third Law).
Extend: any correct new, out-of-vehicle example (e.g., First Law — a book stays on a table; Second Law — kicking a soccer ball harder makes it accelerate more; Third Law — a swimmer pushes water back and moves forward). More than one answer is defensible.

Reward reasoning over a single "right" number. Doubling speed (10 → 20 m/s): Table 1 shows the belted peak force rising from 1,600 N to 4,000 N — more than double (about 2.5×). Strong answers note that more speed means more motion to remove and, if stopping distance grows too, the force does not simply scale one-to-one; accept "more than double" with table support. Heavier rider (50 → 80 kg) at the same speed and deceleration: force increases in proportion to mass (F = ma), e.g., 80/50 = 1.6× the force, because more mass means more inertia to stop. Do not require exact figures; require correct direction and an F = ma / inertia justification.