Constant acceleration

Connect motion graphs with equations, then check what each result means physically.

Work at your own pace through the available lessons, with manual models, short animations and independent questions.

Reading displacement–time graphsRead signed positions, calculate velocities from straight-line slopes and interpret turning points and tangents on displacement–time graphs.
Average speed and velocity from graphsCalculate whole-journey average speed and velocity from displacement graphs, including waiting, reversals, nonzero starting positions and mixed time units.
Velocity–time gradients and accelerationCalculate signed acceleration from velocity–time gradients and separate direction of motion, speed change and zero velocity.
Displacement and distance from velocity–time areasUse signed velocity–time areas for displacement and absolute areas for distance, splitting regions at reversals.
Multistage velocity–time problemsSolve accelerate–cruise–brake problems with stage durations, unknown areas, speed thresholds and halfway positions.
Deriving the constant-acceleration equationsDerive all five SUVAT equations from a straight velocity graph, with signed displacement and a derivation that remains valid at zero acceleration.
Choosing and using SUVAT equationsChoose a constant-acceleration equation from known and required quantities, convert units, keep signs and check physical answers.
Quadratic times and repeated positionsSolve quadratic time equations, interpret repeated positions and reject roots outside the stated motion interval.
Stopping, reversal and total distanceFind a turning time, split the path to calculate total distance and distinguish continued acceleration from braking that ends at rest.
Linked stages of constant accelerationJoin constant-acceleration stages using shared boundary velocities, local durations and cumulative displacement.
Meeting and overtaking on a shared clockFind meeting times by equating positions on common axes, interpret initial coincidence and check candidate times against piecewise motion stages.
Delayed starts and shifted timeWrite delayed-start equations using t minus the delay, reject pre-launch roots and check meetings against later changes of motion.
Vertical motion: signs and assumptionsSet a consistent axis for vertical motion, distinguish positive g from signed acceleration and state the limits of the constant-gravity model.
Drops and downward projectionsCalculate falling times and impact speeds for drops and downward throws, with consistent signs and a model that ends at contact.
Upward projections and maximum heightFind time to maximum height, distinguish rise from ground height, and calculate landing time, impact velocity and total distance.
Times at a height and time above a levelFind both height-crossing times, distinguish a tangent or unreachable level, and restrict time-above intervals to the physical flight.
Meeting particles in vertical motionUse a common ground origin and clock to find vertical meetings, check both particles are in flight, and handle delayed launches.