Sec 3 Physics Kinematics notes

Speed answers "how fast" with a magnitude only; velocity answers "how fast, and which way". A car circling a roundabout at a steady 30 km/h has constant speed but constantly changing velocity, because its direction keeps changing. At O-Level the distinction matters most in one dimension, where the sign carries the direction: +12 m/s to the east and −12 m/s to the west are different velocities with the same speed.

Average speed = distance travelled ÷ time taken. The word average matters: a bus that covers 600 m in 50 s with stops and starts still has an average speed of 12 m/s. Velocity uses displacement — the straight-line change of position — so a runner who completes one lap of a 400 m track in 50 s has an average speed of 8.0 m/s but a zero average velocity, because she ends where she began.

Acceleration is the rate of change of velocity: a = (v − u) ÷ t, where u is the starting velocity and v the finishing one. Uniform acceleration means the velocity changes by equal amounts each second. The units are m/s² — metres per second, every second. A slowing object has a negative acceleration (a deceleration), which is a value, not a different quantity.

A displacement–time graph puts the distance-from-start (upwards) against time (rightwards). The physics lives in the gradient, because velocity is displacement ÷ time — the exact thing a gradient measures on this graph.

To read a velocity from a curve, draw a tangent at the point of interest and find its gradient. A common structured question hands you two points on a tangent ("the tangent passes through (2.0 s, 0 m) and (6.0 s, 24 m)") and expects velocity = 24 ÷ (6.0 − 2.0) = 6.0 m/s. Curves never get a gradient "by eye" — the tangent construction is the method.

A velocity–time graph carries two separate pieces of information. The gradient is acceleration (velocity change per time). The area between the line and the time axis is distance travelled, because each thin slice has height v and width t, and v × t is a small distance; adding the slices collects the whole journey.

For a straight-line graph the area is a rectangle (v × t), a triangle (½ × base × height) or a trapezium made of those pieces — split awkward shapes along a vertical line and add. Keep the units: an area of (m/s) × s comes out in metres.

Near the Earth, any object moving under gravity alone — a free-falling body — accelerates downwards at a constant g ≈ 10 m/s². Air resistance is ignored unless the question says otherwise: a coin and a stone released together land together. Every second of fall adds 10 m/s of downward speed, whether the object started at rest or was thrown.

• Dropped from rest: v = g t (speed after time t) and h = ½ g t² (distance fallen).
• Thrown downwards at u: v = u + g t, and h = u t + ½ g t².
• Thrown upwards at u: the downward acceleration subtracts 10 m/s each second; the object stops at the top when v = 0, at time t = u ÷ g, having risen h = u² ÷ (2g).

Non-uniform acceleration is any motion where equal times do not bring equal velocity changes. The velocity–time graph stops being straight: a steepening curve means the acceleration is growing, a flattening curve means it is shrinking. You are not asked to calculate with curves — only to describe what the shape shows, and to read instantaneous values by drawing tangents.

The classic example is falling with air resistance. At the instant of release the full weight accelerates the object at 10 m/s². As speed grows, drag grows too, so the resultant force — and therefore the acceleration — shrinks: the v–t curve bends over. When drag equals the weight the resultant is zero and the object continues at a constant terminal velocity, shown by the graph flattening into a horizontal line. A skydiver before opening the parachute levels off near 50 m/s; after opening, the much larger drag briefly decelerates her to a new, much slower terminal velocity.