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What is displacement?
The **change in position**: a straight line from start to finish, with a direction (m).
What is distance?
The total length of the path travelled. A size only (m).
Is distance a scalar or a vector?
A **scalar**: a size only.
Is displacement a scalar or a vector?
A **vector**: a size and a direction.
What is velocity?
The **rate of change of position**: how fast, and in which direction (m s⁻¹).
Average speed = ?
Total distance ÷ total time.
Average velocity = ?
Displacement ÷ time taken (Δs ÷ Δt).
Two moves at right angles, x and y. Size of the displacement?
√(x² + y²), by Pythagoras.
What is instantaneous velocity?
The velocity at one moment: the slope of the tangent to the position–time graph at that time.
You finish where you started. What is your average velocity?
**Zero**: the displacement is zero, even though the average speed is not.
What is the unit of speed and of velocity?
**m s⁻¹** (metres per second).
Define acceleration.
The **rate of change of velocity** — how much the velocity changes each second. Unit: m s⁻².
What is the unit of acceleration?
**m s⁻²** (metres per second, every second).
On a velocity–time graph, what is the slope?
The **acceleration**.
On an acceleration–time graph, what is the area under the line?
The **change in velocity**. From rest, that area is the velocity reached.
A flat (horizontal) v–t line means…
Constant velocity → **zero** acceleration.
When does an object slow down?
When its **acceleration is opposite to its velocity**. (If positive is the direction of motion, that means a negative acceleration.)
A downward-sloping v–t line means…
The velocity is **decreasing**. If the velocity is positive the object is slowing down; if it is already negative it is speeding up in the negative direction.
An a–t graph crosses the time axis — what is zero there?
The **acceleration** (not the velocity). The object may still be moving.
Does changing direction count as acceleration?
**Yes** — velocity includes direction, so changing direction changes the velocity.
Formula for acceleration from a graph?
$a = \dfrac{v - u}{t}$ — change in velocity ÷ time.
What is instantaneous acceleration?
The acceleration at one moment: the slope of the **tangent** to the v–t graph at that time.
Uniform or non-uniform acceleration on a v–t graph?
A **straight** line: uniform (constant). A **curved** line: non-uniform.
On a velocity–time graph, what does the area under the line give?
The **displacement** — how far the object travels.
On a velocity–time graph, what does the slope give?
The **acceleration**. (Area = displacement, slope = acceleration — don't swap them.)
What is the given data-booklet formula for displacement from a straight v–t line?
$s = \dfrac{u + v}{2}\,t$ — average velocity × time (the trapezium area).
What does ½(u + v) represent?
The **average velocity** — halfway between the start velocity u and the final velocity v.
Area of a triangle under a v–t line (from rest)?
**½ × base × height** = ½ × time × final velocity.
Area of a rectangle under a flat v–t line?
**speed × time** — a constant velocity gives a rectangular area.
How do you handle an awkward area under a v–t graph?
**Split it** into a rectangle + a triangle, work out each, then **add** them.
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