1.14PH1 · Section 1: Forces and motion

Speed, velocity and acceleration

Key learnings

Speed is scalar; velocity is a vector
Speed = distance per unit time; $\text{speed} = d/t$ ; unit m/s; a scalar (magnitude only). Velocity = speed in a given direction; unit m/s; a vector (magnitude + direction). The mark scheme needs BOTH: magnitude AND a stated direction — 30 m/s north and 30 m/s south share a speed but have opposite velocities. Average speed = total distance / total time; instantaneous speed = the gradient of a distance–time graph at that instant.
Acceleration and the SUVAT equations
Acceleration = change in velocity per unit time: $a = (v - u)/t$ ; unit m/s²; a vector. Deceleration is negative acceleration. The four SUVAT equations (uniform $a$ ): $v = u + at$ ; $v^2 = u^2 + 2as$ ; $s = ut + \frac{1}{2}at^2$ ; $s = \frac{1}{2}(u + v)t$ , where $s$ = displacement (m), $u$ = initial velocity, $v$ = final velocity (m/s), $a$ = acceleration (m/s²), $t$ = time (s). E.g. $u = 0$ , $a = 2$ , $t = 3$ : $v = 0 + 2 \times 3 = 6$ m/s.
Free-fall acceleration g ≈ 9.8 m/s²
Near the Earth's surface, all objects in free fall (no air resistance) accelerate downward at $g \approx 9.8 \text{ m/s}^2$ , the same for every mass (feather and hammer fall together in a vacuum). If dropped from rest, $u = 0$ . Weight $W = mg$ (mass in kg) is a force in newtons (N), not a mass. The formula sheet gives $g = 9.8 \text{ m/s}^2$ ; use $10 \text{ m/s}^2$ only if stated. E.g. from rest after 2 s, $v = gt = 9.8 \times 2 = 19.6$ m/s.

Common mistakes

Drawn from real examiner reports.

Velocity defined without direction

Writing "velocity is how fast an object moves" or "the speed of an object" scores zero — the mark scheme also needs the direction. The full form is "the speed of an object in a stated direction" (two elements: speed + a direction). "A vector version of speed" on its own is too vague. Speed is the scalar; velocity is the vector that carries the direction.

Recurring across multiple Paper 1P examiner reports — June 2024 and November 2024 both note that candidates who give vague definitions of physical quantities score zero on definition questions because they omit the second element required for two marks.

Acceleration is not just speeding up

Acceleration is the rate of change of velocity, not merely "getting faster". Two elements are required: (1) rate (per unit time); (2) change in velocity (a vector). A braking car has acceleration (negative), and an object circling at constant speed has centripetal acceleration because its direction changes. Mark-scheme form: $a = (v - u)/t$ ; unit m/s².

Recurring error across all Paper 1P examiner reports — the examiner consistently notes that weaker candidates describe acceleration only as "speeding up" without recognising deceleration or the vector nature of velocity.

Not squaring v (v vs v²)

In $v^2 = u^2 + 2as$ you must square the velocity terms, and in $\text{KE} = \frac{1}{2}mv^2$ you square $v$ before multiplying. Confusing $v$ with $v^2$ , or forgetting the final square root (leaving $v^2 = 24$ instead of $v = 4.9$ m/s), is a repeated slip. Substitute first, then square or take the root carefully.

November 2024 Paper 1P Q2(a): weaker candidates made mistakes when calculating kinetic energy by not squaring the speed — a parallel error to entering the wrong power of velocity in SUVAT and energy equations.

Deceleration sign left positive

When an object slows down, enter the acceleration as negative (e.g. $a = -3$ m/s², not $+3$ ). In $v^2 = u^2 + 2as$ a braking car needs $a < 0$ ; using $+3$ gives a final speed larger than the start, which fails the sense-check. Deceleration and negative acceleration mean the same thing — carry the minus sign through every SUVAT step.

v-t graph: gradient vs area swapped

On a velocity–time graph the gradient = acceleration (m/s²) and the area under the line = displacement (m). Candidates routinely swap them — finding the area when asked for acceleration, or the gradient when asked for distance. Think: gradient = rate of change (acceleration); area = the accumulated distance.

Distance vs displacement

Distance is total path length (a scalar, always ≥ 0). Displacement is the straight-line distance from start to finish in a stated direction (a vector, can be negative). One lap of a 400 m track gives distance = 400 m but displacement = 0 m. Speed pairs with distance; velocity pairs with displacement.

Exam tips

List SUVAT before choosing an equation
Write out $s, u, v, a, t$ ; mark the three known values and the one unknown; then pick the single equation containing exactly those four symbols. This stops you reaching for $v = u + at$ when $t$ is not given and hitting two unknowns in one equation.
Substitute numbers before rearranging
Quote the formula, put the numbers in first, then rearrange. Candidates who rearrange algebraically first and slip score zero, whereas substituting first still earns the substitution mark even when the rearrangement that follows is wrong.
Sense-check units, sign and direction
A braking object must end slower; a dropped object starts at $u = 0$ ; a speed needs the unit m/s (not m/s²); a velocity answer needs a direction. Running each result past these quick checks catches most of the marks lost to careless slips.

Revision notes