Answers · Acceleration, falling and drag

Acceleration, falling and drag — return questions key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. FR1 · Return

Model answer. (a) Acceleration is the change in velocity per unit time, a = Δv / Δt, measured in m/s². (b) The gradient is the acceleration: rise ÷ run = (7.0 − 3.0) m/s ÷ 2.0 s = 2.0 m/s². (c) A straight rising line: constant acceleration. A rising curve that gets flatter: changing acceleration, speeding up by less each second. A flat line: constant speed, zero acceleration. A straight falling line: constant deceleration. (d) a = (10 − 25) m/s ÷ 5.0 s = −15 m/s ÷ 5.0 s = −3.0 m/s², a deceleration of 3.0 m/s². (e) Friction between the solid surfaces: it acts against the motion, so it slows the disc, and it heats the disc. (f) g ≈ 9.8 m/s²: the stone gains about 9.8 m/s of speed in every second, whatever its mass.

A full answer includes

(a) Acceleration is the change in velocity per unit time; unit m/s².
(b) Gradient = (7.0 − 3.0) m/s ÷ (2.0 − 0) s = 2.0 m/s².
(c) Straight rising: constant acceleration. Rising curve getting flatter: changing acceleration, speeding up by less each second. Flat: constant speed, zero acceleration. Straight falling: constant deceleration.
(d) (10 − 25) m/s ÷ 5.0 s = −3.0 m/s²: a deceleration of 3.0 m/s².
(e) Friction (solid friction): it acts against the motion, slowing the disc, and it heats the disc.
(f) About 9.8 m/s²: the speed grows by about 9.8 m/s in every second.

Also accept

(a) change in velocity per unit time, m/s²; (b) 2.0 m/s²; (d) −3.0 m/s², 3.0 m/s²; (e) friction, heats; (f) 9.8 m/s²

Watch for

“(b) 7.0 ÷ 2.0 = 3.5 m/s².” — She did not start from rest. Use the change in speed, 7.0 − 3.0 = 4.0 m/s.
“(d) The deceleration is −3.0 m/s².” — The acceleration is −3.0 m/s²; the deceleration is its size, 3.0 m/s². Saying "deceleration" already says it is slowing down.

2. FR2 · Return

Model answer. (a) Drag is the friction of a liquid or a gas: a force that acts against the motion of an object moving through it. Drag in air is called air resistance. (b) A bigger speed, a bigger or more spread-out shape, and a liquid instead of a gas all give more drag. (c) Speed = 0.20 m ÷ 0.80 s = 0.25 m/s. (d) Terminal velocity is the constant speed a falling object reaches when the drag on it has grown so much that the forces on it balance, so the speed stops changing. In air, the air resistance is then as big as the weight: equal and opposite. (e) Without air resistance the speed rises in a straight line, 9.8 m/s every second. With air resistance the curve starts just as steep, then gets flatter and flatter and levels off at the terminal velocity. (f) The parachute makes the air resistance much bigger than her weight, so she decelerates. As she slows, the air resistance gets smaller, until it equals her weight again: she falls at a new, lower terminal velocity.

A full answer includes

(a) Drag is the force that acts against the motion of an object moving through a liquid or a gas; drag in air is air resistance.
(b) Any two: a bigger speed; a bigger size or a more spread-out shape; moving through a liquid instead of a gas.
(c) 0.20 m ÷ 0.80 s = 0.25 m/s.
(d) The constant speed a falling object reaches when the drag on it has grown so much that the forces on it balance (in air: the air resistance is as big as its weight); its speed then stops changing.
(e) Without air resistance: a straight line from 0 with gradient 9.8 m/s². With air resistance: a curve that starts with the same gradient, gets flatter and levels off at the terminal velocity.
(f) She slows down to a new, lower steady speed: the air resistance becomes bigger than her weight, then falls as she slows until it equals her weight again, at a lower terminal velocity.

Also accept

(a) drag, air resistance; (c) 0.25 m/s; (d) steady speed when the forces balance (in air, air resistance = weight); (f) slows to a lower terminal velocity

Watch for

“(d) At terminal velocity there are no forces on the object.” — The forces still act: its weight, and a drag that has grown until the forces balance.
“(f) She goes up when the parachute opens.” — She keeps falling and only slows down, to a new, lower terminal velocity.