Average speed = distance / time (scalar vs vector)
Average speed = distance / time, unit m/s. Speed is a SCALAR (magnitude only); velocity is a VECTOR — speed in a stated direction (magnitude AND direction). Two cars travelling at 30 m/s in opposite directions have the same speed but opposite velocities. The SI base units are the metre (m), the second (s), m/s for speed and velocity, and m/s^2 for acceleration. Always convert km to m and minutes or hours to s BEFORE substituting into any equation.
Acceleration a = (v - u)/t; gradients on motion graphs
Acceleration is the rate of change of velocity: a = (v - u)/t (u = initial velocity, v = final velocity, t = time); the unit is m/s^2 and a negative value means deceleration. On a DISTANCE-time graph the gradient equals the speed. On a VELOCITY-time graph the gradient equals the acceleration and the AREA under the line equals the distance travelled. For a curved velocity-time graph the instantaneous acceleration is the gradient of the TANGENT.
v^2 = u^2 + 2as — uniform acceleration only
v^2 = u^2 + 2as links the final velocity v, initial velocity u, acceleration a and distance s, and is used when the time is not given. It is valid ONLY for uniform (constant) acceleration: if a velocity-time graph is curved the acceleration is changing, so the equation must not be used and the distance is the AREA under the graph instead. Substitute first, then rearrange (with u = 0, v = square root of 2as); do not forget the final square root.
Drawn from real examiner reports.
v^2 = u^2 + 2as on a curved graph
v^2 = u^2 + 2as assumes CONSTANT acceleration. Applied to a curved (non-uniform) velocity-time section it earns no credit — candidates who did so scored zero. Where the acceleration is genuinely uniform the equation is fine and is credited. To find the distance under a curve, estimate the AREA instead: count grid squares, or split the region into triangles and rectangles.
Jun 2024 1P Q12b (applied to a curved section, no credit); credited where acceleration is uniform, Jun 2023 1P Q9b(ii).
Gradient vs area on a v-t graph
On a velocity-time graph the two rules are easy to swap: the GRADIENT gives the acceleration and the AREA under the line gives the distance travelled. If the question asks how far the object went, find the area (a trapezium for a straight line, counting squares for a curve) — not the slope. Finding a gradient when the distance was required scores nothing.
Jun 2024 1P Q12b (found a gradient instead of the area under the curve).
Acceleration off a curve needs a tangent
On a CURVED velocity-time graph the acceleration at an instant is the gradient of a TANGENT drawn at that point. Many candidates instead read a single velocity and time straight off the curve and divided them as a = v/t, which was not credited. The marks are for an accurately drawn tangent and the gradient calculated from it.
Jun 2024 1P Q12a.
Speed vs velocity (scalar vs vector)
A "define velocity" or "speed versus velocity" question needs the vector idea. Velocity = speed in a stated DIRECTION (magnitude and direction); writing "how fast something moves" scores zero because it omits direction and merely restates speed, a scalar. A consequence: an object moving in a circle at constant speed has continuously changing velocity, so it is accelerating.
Wrong sketch: line through the origin
A frequent sketch error is drawing a straight line of positive gradient through the origin whatever the context — here for an object that was actually slowing down. Match the SHAPE of the graph to the described motion: decelerating slopes downwards, constant velocity is horizontal, and uniform acceleration from rest is a straight line rising from the origin.
Nov 2024 1P Q2b(i).
v^2 = u^2 + 2as substitution slips
Even with the correct equation, substitution slips lose marks on v^2 = u^2 + 2as: silently changing the final velocity from 0 to a non-zero value, and rearrangement arithmetic errors such as writing 169 - 20 = 149. Substitute the data FIRST and rearrange afterwards, so a method mark survives an algebra slip.
Jun 2024 1PR Q9c(i).
Substitute first, then rearrange
Write the equation, substitute the data, THEN rearrange. Candidates who rearranged first and slipped scored zero, while those who substituted first kept the substitution mark even when the algebra went wrong. It also guards against quoting the reciprocal of the answer.
Pick the right motion equation
Choose the equation from what is given. No time and constant acceleration: use v^2 = u^2 + 2as. Time given: use a = (v - u)/t, or the trapezium area s = (1/2)(u + v)t for distance. Never use v^2 = u^2 + 2as on a curved (non-uniform) graph.
Match the command word and mark tariff
Let the mark tariff guide how many points to give. "Describe" states what happens; "explain" needs reasons (balanced forces, so zero resultant force, so zero acceleration, so constant velocity). Simply repeating the wording of the question earns nothing.
Graph scaffold
For any motion graph: (1) identify the type — distance or velocity on the y-axis? (2) Label both axes with quantity AND unit. (3) Distance-time: gradient = speed. (4) Velocity-time: gradient = acceleration, area = distance. Do not read the wrong rule off the wrong graph.
| Quantity | Symbol | Formula | SI unit |
|---|---|---|---|
| Average speed | m/s | ||
| Acceleration | m/s^2 | ||
| Uniform-acceleration relation | — | — | |
| Distance from a straight v-t line | (trapezium area) | m |
Where = initial velocity (m/s), = final velocity (m/s), = time (s), = distance (m), = acceleration (m/s^2).
SI units to memorise: distance in metres (m), time in seconds (s), speed/velocity in m/s, acceleration in m/s^2. Convert km to m and minutes/hours to s before substituting.
Scalar vs vector: distance and speed are scalars (magnitude only); displacement and velocity are vectors (magnitude AND direction).
Define average speed and give its formula and unit.
A train travels a distance of 6000 m in a time of 300 s.
Calculate the average speed of the train. Give the unit of your answer.
