Theme A — Space, Time and Motion
A.1.2 Speed and Velocity — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 4 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.1.2 Speed and Velocity — IB PHYSICS SL notes: Define and calculate speed, average speed, velocity, average velocity and instantaneous velocity, and relate them to displacement–time graphs.Speed = the distance travelled per unit time; it is a scalar with SI unit m s−1.It has mag…
- Speedometer reading
- Sign of velocity
- Instantaneous speed
- Average values
- Drawing a tangent
- Horizontal line
Part 1 of 8Speed
Speed
Speed the distance travelled per unit time; it is a scalar with SI unit m s−1.
- It has magnitude only, so it carries no direction and can never be negative.
- Other units are km h−1 and mph; 1 km h−1 = 1/3.6 m s−1.
Average speed
- Average speed total distance divided by total time taken.
- average speed = total distance / total time.
- The total time includes any stops, so a long wait lowers the average speed.
Speedometer reading
- Speedometer reading a car speedometer shows the instantaneous speed at one moment.
Part 2 of 8Velocity
Velocity
Velocity the rate of change of displacement; it is a vector with unit m s−1.
- Its direction is the direction of the displacement.
Average velocity
- Average velocity v = s / t, where s is the total displacement and t the total time.
- For constant acceleration it can also be found from average velocity = (u + v) / 2, where u is the initial and v the final velocity.
- Over a round trip the displacement is zero, so the average velocity is zero although the average speed is not.
Sign of velocity
- Sign of velocity in one dimension the sign gives the direction.
- With right as positive, v = −3 m s−1 means moving left at 3 m s−1.
- A change of sign means the object has reversed direction, but its speed is only the magnitude.
Part 3 of 8Speed compared with velocity
| Quantity | Speed | Velocity |
|---|---|---|
| Type | Scalar | Vector |
| Defined from | Distance | Displacement |
| Direction | None | Required |
| Sign | Never negative | Positive or negative |
| Two cars | Equal speeds in opposite lanes | Different velocities because the directions differ |
Part 4 of 8Instantaneous and average values
Instantaneous velocity
- Instantaneous velocity the velocity at one moment, found by taking a very short time interval (Δt → 0).
- On a displacement–time graph it equals the gradient of the tangent drawn at that time.
- For constant velocity the graph is a straight line, so the instantaneous and average velocities are equal.
Instantaneous speed
- Instantaneous speed the magnitude of the instantaneous velocity.
Average values
- Average values they describe a whole interval and can hide detail.
- Average speed is not generally the magnitude of average velocity, because distance and displacement can differ.
- The average velocity on a curved s–t graph is total displacement divided by total time, the gradient of the chord.
Drawing a tangent
- Drawing a tangent it should just touch the curve at the required point.
- The angle between the curve and the tangent should be roughly equal on both sides of the point.
- A large gradient triangle is used to reduce the uncertainty.
Part 5 of 8Displacement–time graph readings
1Horizontal line
- Horizontal line the object is at rest.
2Straight sloping line
- Straight sloping line constant velocity; a steeper line means a greater speed.
3Curve with increasing gradient
- Curve with increasing gradient the object is speeding up.
4Negative gradient
- Negative gradient motion in the negative direction.
Part 6 of 8Relative velocity
Relative velocity
- Relative velocity the velocity of object A as measured from object B is vA − vB, where both are measured relative to the ground.
- Two trains moving the same way at 30 and 25 m s−1 approach one another at 5 m s−1.
- Moving in opposite directions, the closing speed of the same trains is 55 m s−1.
Two dimensions
- Two dimensions the subtraction is a vector subtraction, solved with a triangle of velocities.
- A boat crossing a flowing river is the standard case.
Part 7 of 8Measuring speed
Light gate
- Light gate a card of length ℓ blocks the beam for a time t, so v ≈ ℓ / t.
Motion sensor
- Motion sensor it records position against time and the speed is found from the data.
Timing a known distance
- Timing a known distance it gives an average speed over the interval.
- The result approaches the instantaneous value when the interval is short.
Typical values
- Typical values walking 1.5 m s−1, sprinter about 10 m s−1, motorway car 30 m s−1, sound in air 340 m s−1.
Part 8 of 8More from the specification
More from the specification
Measurement speed range
- Measurement speed range light gates record instantaneous vehicle speeds across a wide calibrated experimental range with minimal human reaction error.
Projectile motion independence
- Projectile motion independence horizontal velocity remains constant in negligible air resistance,
- while vertical motion undergoes constant gravitational acceleration.
Maximum projectile height
- Maximum projectile height at the apex of projectile trajectory, instantaneous vertical velocity component falls momentarily to zero.
Kinematics equations of motion
- Kinematics equations of motion uniform acceleration equations relate displacement, initial velocity, terminal velocity, and elapsed transit time.
Projectile Motion Components
- In projectile motion under gravity, horizontal motion proceeds at constant horizontal velocity (ax = 0),
- while vertical motion experiences constant gravitational acceleration.
- (ay = -9.81 m s⁻²)
Maximum Height Calculation
- The maximum vertical height attained by a projectile launched at angle θ with speed u is determined using the kinematic suvat equation vy² = uy² - 2gh,
- where vertical velocity vy = 0 at the peak.
Air Resistance and Terminal Velocity
- For a projectile or falling body moving through air, drag force increases with speed until it equals downward weight;
- at this point, resultant force is zero and terminal velocity is reached.
Motion on an Inclined Plane
- An object or cyclist accelerating along a frictionless slope experiences a driving component of gravity parallel to the incline equal to F = mg sin θ,
- producing acceleration a = g sin θ.
Fluid resistance
- Drag force from a fluid opposing motion.
Projectile
- Object moving under gravity alone in two dimensions.
Resistance
- Opposition to current, R = V / I, in ohms (Ω).
Terminal
- Connection point of a cell, labelled + or −.
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.
Kinematic equations
- Equations relating displacement, velocity, acceleration and time for constant acceleration.
Velocity-time graph
- A graph of velocity against time whose gradient is acceleration and area is displacement.
Key terms
| Term | Meaning |
|---|---|
| Speed | Rate of change of distance; a scalar |
| Velocity | Rate of change of displacement; a vector |
| Average velocity | Total displacement divided by total time |
| Instantaneous velocity | Velocity at one moment; gradient of the tangent on an s–t graph |
| Relative velocity | Velocity of one object as measured from another object |
| Gradient | Change in the vertical quantity divided by change in the horizontal quantity |
Avoid these mistakes
1
Averaging speeds by adding them and halving — use total distance divided by total time.
2
Quoting a velocity without a direction — a velocity must state its direction or sign.
3
Reading the gradient of a distance–time graph as velocity — it gives speed only; displacement–time gives velocity.
4
Forgetting to convert km h−1 to m s−1 — divide by 3.6.
5
Assuming zero average velocity means no movement — it only means zero net displacement.
Marked practiceQuizzes for this lesson
Last updated:
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).