KCSE 2025 Physics P1 Q19 — Free Fall, Momentum & Estimating Length
Published
The Question
“This is the final Section B question, in three parts. (a) A stone and a piece of paper are dropped together in a vacuum and land at the same time; explain this observation. (b) A car of mass 1560 kg travelling at 25 m/s is brought to rest by a constant braking force of 3000 N. (b)(i) Calculate the change in momentum of the car. (b)(ii) Calculate the time taken for the car to stop. (c) Jane's palm is 18.7 cm long; describe how she can use it to estimate the length of a table, and explain why the estimate is not accurate.”
(a) Explain why the stone and paper fall together
In a vacuum there is no air, so there is no air resistance to slow the paper down. The only force acting on each object is gravity, and the acceleration due to gravity is the same for every object regardless of its mass. With the same acceleration and no drag, the stone and the paper fall together and land at the same time.
(b)(i) Calculate the change in momentum
The change in momentum is the mass multiplied by the change in velocity, m(v − u). The car of mass 1560 kg slows from an initial velocity of 25 m/s to a final velocity of 0, so substituting gives the change in momentum. The negative sign shows the momentum decreases as the car is brought to rest.
(b)(ii) Calculate the time to stop
The impulse of the braking force, force multiplied by time, equals the change in momentum. Rearranging for time gives the size of the momentum change divided by the force. Dividing 39000 by 3000 gives the stopping time.
(c) Estimate the table length with a palm
Jane knows her palm is 18.7 cm long. She lays her palm end to end along the edge of the table, counts how many palm-lengths fit along it, and multiplies that count by 18.7 cm to get an estimate of the table's length.
(c) Explain why the estimate is not accurate
The estimate is not accurate because small gaps or overlaps between successive placements of the palm add up to a cumulative error along the whole length. On top of this, a palm is not a standard, precise measuring tool, so the result cannot be trusted for exact work.
Final Result
In a vacuum both objects fall with the same gravitational acceleration and no air resistance, so they land together. The change in momentum of the car is −39000 kg·m/s (a decrease of 39000 kg·m/s), and the time taken to stop is 13 s. The table length is estimated as (number of palm-lengths) × 18.7 cm, but the method is imprecise.
Why this method works
Free fall in a vacuum reveals that gravity accelerates all masses equally: a heavier object feels a larger gravitational force but also has proportionally more inertia to overcome, and the two effects cancel, leaving the same g for everything. It is only air resistance — absent in a vacuum — that normally makes light, wide objects like paper fall slowly. The braking problem uses the impulse–momentum theorem, Ft = Δp, which is just Newton's second law written over a time interval: a fixed force removes momentum at a steady rate, so the stopping time is simply the momentum to be removed divided by the force. The palm example shows why physics insists on standard units: a body part varies from person to person and accumulates gap-and-overlap errors, so it can estimate but never accurately measure.
Cross-check with F = ma: the deceleration is F/m = 3000/1560 ≈ 1.92 m/s², and time to lose 25 m/s at that rate is 25/1.92 ≈ 13 s, agreeing with the impulse method.