Physical quantities and kinematics

2. Kinematics

5 min read 12 parts Lesson 22 of 22 Unit quiz

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Lesson summary

2. Kinematics — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Describe motion with distance, displacement, speed, velocity and acceleration, interpret motion graphs, use the equations of motion, and analyse free fall and projectiles.Distance — how far an object trav…

Average acceleration
Always check the axes
Displacement–time
Velocity–time
Acceleration–time
Gradient of s–t

Section 1 of 12Distance and displacement

Distance
- how far an object travels along its path; a scalar with magnitude only.
Displacement
- the change in position from the start, with direction; a vector.
- A 300 m race on a 400 m track gives a distance of 300 m but a displacement of 100 m from the start.
- If the athletes ran the full 400 m, their displacement would be zero.

Section 2 of 12Speed and velocity

Speed
- distance travelled per unit time; average speed = total distance ÷ time taken; a scalar in m s⁻¹ .
  - (km h-1 or mph are also used)
Velocity
- the rate of change of displacement; a vector, speed in a given direction.
- Average velocity vavg = Δx/Δt.
- For constant acceleration, vavg = (u + v)/2.
Caution
- average velocity is not average speed with a direction, because distance and displacement can differ greatly for the same motion.

Section 3 of 12Acceleration

Acceleration
- the rate of change of velocity; a vector measured in m s⁻².
Average acceleration
- a = Δv/Δt = (v − u)/t, where u is the initial and v the final velocity.
- Acceleration occurs if the speed or the direction changes; slowing down is deceleration (negative acceleration in the direction of motion).

Section 4 of 12Motion graphs: what slope and area mean

Graph	Gradient (slope)	Area under graph
Distance–time	Speed (never negative)	Meaningless
Displacement–time	Velocity	Meaningless
Speed–time	Acceleration	Distance travelled
Velocity–time	Acceleration	Displacement
Acceleration–time	Meaningless (jerk)	Change in velocity

Always check the axes
- distance and displacement graphs, and speed and velocity graphs, look similar but mean different things.

Section 5 of 12Reading shapes on graphs

Displacement–time
- a straight diagonal line is constant velocity, a curve is acceleration, a horizontal line is rest; a negative slope means motion in the negative direction.
Velocity–time
- a horizontal line is constant velocity, a straight sloping line is uniform acceleration, a curve is changing acceleration; the y-intercept is the initial velocity.
Acceleration–time
- a horizontal line means constant acceleration, a gap on the axis (zero) means constant velocity.
- A change in sign of velocity shows that the object has reversed direction.

Section 6 of 12Gradients and areas in calculations

Gradient of s–t
- velocity; a steeper slope is a greater velocity.
Gradient of v–t
- acceleration = Δv/Δt; the larger the gradient the larger the acceleration.
Area under v–t
- displacement; split the area into triangles (½bh) and rectangles (bh).
- Convert units (km h-1 to m s⁻¹, mm or cm to m) before calculating.

Section 7 of 12Equations of uniformly accelerated motion

Variables
- s displacement, u initial velocity, v final velocity, a acceleration and t time; the acceleration must be constant.

Equation	Missing variable	Derivation
v = u + at	s	Gradient of the v–t line is a
s = ½(u + v)t	a	Area of a trapezium (average velocity × time)
s = ut + ½at2	v	Area as a rectangle ut plus a triangle ½at2
v2 = u2 + 2as	t	Eliminate t from the other equations

Only s = ut + ½at2 and v2 = u2 + 2as are in the data booklet, so remember the others.

Section 8 of 12Solving problems with the equations

List the known and unknown variables, using context: a vertical fall has a = 9.81 m s⁻², and starting or finishing at rest means u = 0 or v = 0.
Choose the equation that contains the quantities listed and not the one you do not need.
Convert to SI units, substitute and rearrange.
Check signs: choose a positive direction and keep it, so deceleration appears as a negative value of a.

Section 9 of 12Experiment: measuring g with light gates

Aim
- find the acceleration of free fall g from the time a ball bearing takes to fall a measured height.
Variables
- independent: height h; dependent: time t; controlled: the same ball bearing, the same electromagnet and the same distance from ball to the top of the tube.
Equipment
- metre ruler, steel ball bearing, electromagnet, two light gates, timer (0.01 s), clamp stand, glass tube, cushion.
  - (1 mm resolution)
- Fix the electromagnet at the top of the clamp stand and the glass tube vertically below it; switch the current on only after everything is set up.
- Place two light gates a distance h apart (start at about 10 cm) and measure h with a metre ruler.
- Hold the ball against the electromagnet, then switch off to release it; the timer starts at the first gate and stops at the second.
- Record t, increase h by about 5 cm, and use 5 to 10 heights, repeating each at least 3 times to find an average t.

Section 10 of 12Analysing the g experiment

Straight-line form
- s = ut + ½at2 with s = h and a = g becomes 2h/t = gt + 2u.
- Plot y = 2h/t against x = t.
- The gradient is g and the y-intercept is 2u (u is the speed at the first gate).
Systematic error
- residual magnetism after the electromagnet is switched off can make t longer than it should be.
Random errors
- a 1 mm ruler, parallax when reading h, and the ball not falling through the centre of each gate; repeat readings and average.
Safety
- keep water away from the electromagnet, switch on only when set up, use a cushion to protect the floor and ball,
  - and clamp the stand to the bench with a G-clamp.

Section 11 of 12Projectile motion

Independence
- the vertical and horizontal motions are independent and are analysed separately.
- Horizontal: no force, so constant velocity and a = 0 (v = s/t).
  What the symbols mean: v = speed (m s⁻¹) · d or s = distance (m) · t = time (s)
- Vertical: only gravity acts, so a = 9.81 m s⁻² downward.
Key terms
- time of flight, maximum height (where the vertical velocity is momentarily zero) and range (horizontal distance travelled).
  - (time in the air)
Three cases
- vertical projection, horizontal projection from a height, and projection at an angle.
Angled launch
- resolve u into u cos θ (horizontal) and u sin θ (vertical) before using the equations.

Section 12 of 12More from the specification

Velocity-time graph
- A graph of velocity against time whose gradient is acceleration and area is displacement.
Displacement-time graph
- A graph of displacement against time whose gradient is velocity.
Acceleration-time graph
- A graph of acceleration against time whose area is the change in velocity.

Last updated: 14 October 2026