Theme A — Space, Time and Motion
A.1.4 Kinematic Equations — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 6 of 63 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
A.1.4 Kinematic Equations — IB PHYSICS SL notes: Select and apply the equations of uniformly accelerated motion (suvat) to solve problems in one dimension.Kinematic equations — four equations describe any motion with constant (uniform) acceleration in a straight line.s — displace…
- Choosing an equation
- Data booklet
- v = u + at
- What the symbols mean
- s = ½(u + v)t
- s = ut + ½at2
Part 1 of 8The five variables
Kinematic equations
- Kinematic equations four equations describe any motion with constant (uniform) acceleration in a straight line.
s
s displacement in m.
u
u initial velocity in m s−1.
v
v final velocity in m s−1.
a
a acceleration in m s−2.
t
t time interval in s.
Part 2 of 8The four equations
| Equation | Variable it leaves out |
|---|---|
| v = u + at | s |
| s = ut + ½at2 | v |
| v2 = u2 + 2as | t |
| s = ½(u + v)t | a |
Choosing an equation
- Choosing an equation pick the one that contains the three known values and the one wanted, and leaves out the fifth variable.
Data booklet
- Data booklet these equations are given in the data booklet and need not be memorised.
Part 3 of 8Where the equations come from
v
v u + at
- it is the definition of acceleration rearranged.What the symbols mean: v = final velocity (m s−1) · u = initial velocity (m s−1) · a = acceleration (m s−2) · t = time (s)
s
½(u + v)t
- on a straight v–t graph the displacement is the area of a trapezium of average height ½(u + v) and width t.What the symbols mean: s = displacement (m) · u = initial velocity · v = final velocity (m s−1) · t = time (s); (u + v)/2 is the average velocity
s
s ut + ½at2
- substitute v = u + at into s = ½(u + v)t.What the symbols mean: s = displacement (m) · u = initial velocity (m s−1) · a = acceleration (m s−2) · t = time (s)
v2
v2 u2 + 2as
- eliminate t between the first and fourth equations.What the symbols mean: v = final velocity · u = initial velocity (m s−1) · a = acceleration (m s−2) · s = displacement (m)
Validity
- Validity the equations hold only when acceleration is constant.
- They fail when the engine force changes or air resistance grows.
Part 4 of 8Hidden information in the wording
1Starts from rest
- Starts from rest u = 0.
2Comes to rest
- Comes to rest v = 0.
3Dropped
- Dropped u = 0 and a = g.
- (positive downwards if down is positive)
4Falling due to gravity
- Falling due to gravity a = 9.81 m s−2 in the chosen sign convention.
5Constant speed
- Constant speed a = 0.
6Constant acceleration in a straight line
- Constant acceleration in a straight line a signal that the kinematic equations apply.
Part 5 of 8Method for solving problems
1
Choose a positive direction and use it for every vector (s, u, v and a).
2
Write down the known and unknown quantities, using the context to find hidden values.
3
Select the equation that contains the listed quantities and omits the fifth.
4
Convert units to SI, substitute, and rearrange to solve.
5
Check that the answer is reasonable and that its sign matches the direction.
Part 6 of 8Free fall and vertical motion
Free fall and vertical motion
Acceleration of free fall
- Acceleration of free fall near Earth's surface, with air resistance ignored, every object accelerates at g = 9.8 m s−2 downwards.
- The equations use a = +g or a = −g depending on the sign convention.
Object thrown upwards
- Object thrown upwards with up positive, a = −9.8 m s−2 and the velocity is zero at the top.
- The time up equals the time down when it returns to the same height.
Quadratic in t
- Quadratic in t s = ut + ½at2 often has two roots.
- Reject a negative time, or note that the roots may be the upward and downward passes.
Part 7 of 8Stopping distance and multi-stage motion
1Braking distance
- Braking distance with v = 0, s = u2 / (2|a|).
- Doubling the initial speed quadruples the braking distance for the same deceleration.
2Two-stage motion
- Two-stage motion the final velocity of one stage is the initial velocity of the next.
- Treat each stage with its own suvat values, then add the displacements or times.
3Two objects meeting
- Two objects meeting write each displacement in terms of the same time t and equate them.
- This gives a single equation, often a quadratic.
Part 8 of 8More from the specification
More from the specification
Independent 2D projectile components
- Independent 2D projectile components a launched projectile travels at constant horizontal speed while uniform gravitational acceleration governs its vertical trajectory.
Terminal velocity of a falling skydiver
- Terminal velocity of a falling skydiver upward aerodynamic drag eventually equals downward weight,
- causing the skydiver to descend at constant terminal velocity.
Interpreting motion graphs and gradients
- Interpreting motion graphs and gradients on displacement-time graphs, tangent slope represents instantaneous velocity,
- while velocity-time gradient indicates instantaneous acceleration.
Kinematic equations for uniform acceleration
- Straight-line motion under constant acceleration satisfies v = u + at, s = ut + 0.5at2, and v2 = u2 + 2as.
Projectile motion independence
- Horizontal motion occurs at constant velocity (ax = 0), while vertical motion experiences constant gravitational acceleration (ay = -g).
Terminal velocity and fluid drag
- As an object accelerates through fluid, drag force increases until balancing downward weight,
- resulting in zero net acceleration and constant terminal velocity.
Scalar quantity
- A quantity with magnitude only, such as potential
Projectile
- Object moving under gravity alone in two dimensions.
Terminal
- Connection point of a cell, labelled + or −.
Gradient
- Slope of a graph line.
Terminal velocity
- Constant speed when air resistance equals weight.
Maximum height
- The greatest height reached, where the vertical velocity is zero.
Projectile motion
- Two-dimensional motion with constant horizontal velocity and vertical acceleration g.
Velocity-time graph
- A graph of velocity against time whose gradient is acceleration and area is displacement.
Fluid resistance
- Drag force from a fluid opposing motion.
Key terms
| Term | Meaning |
|---|---|
| Uniform acceleration | Constant acceleration, required for the suvat equations |
| suvat | Shorthand for displacement s, initial velocity u, final velocity v, acceleration a and time t |
| Free fall | Motion under gravity only |
| Braking distance | Distance travelled while decelerating to rest |
| Initial velocity | Velocity at t = 0 |
| Sign convention | Choice of positive direction applied to all vectors |
Avoid these mistakes
1
Using the equations when acceleration is not constant — they apply only to uniform acceleration.
2
Mixing sign conventions, for example using +g with up positive — keep one convention throughout.
3
Forgetting hidden values — at rest means u = 0 or v = 0.
4
Dropping the square on t or on the velocities — v2 = u2 + 2as and s = ut + ½at2.
5
Choosing an equation with an unwanted unknown — choose the one that omits the unneeded variable.
Marked practiceQuizzes for this lesson
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