Motion

Imagine you walk 400 m east to a friend's house, then 300 m back west to a café in between. How far did you walk? How far are you from home now?

The distance you walked is the total path length: 400 + 300 = 700 m. The displacement is your final position relative to your start point — only 100 m east of home. Distance has only a size (it is a scalar); displacement has both size and direction (it is a vector).

This distinction matters in MYP Sciences. Examiners often build questions around someone moving in two directions and then ask separately for distance and displacement. They are usually different numbers.

A useful test: if the question asks "how far?", they usually want distance. If it asks "how far from start?" or "what is the resultant?", they want displacement.

Speed is the distance covered per unit time:

$\text{speed} = \frac{\text{distance}}{\text{time}} \quad\text{(m/s)}$

Velocity is the displacement per unit time, so it carries a direction:

$\text{velocity} = \frac{\text{displacement}}{\text{time}} \quad\text{(m/s, with direction)}$

Two cyclists pedalling at 5 m/s on the same straight road have equal speeds, but if they are heading in opposite directions their velocities are equal in size and opposite in sign (e.g. +5 m/s vs −5 m/s).

Acceleration is how quickly velocity changes:

$a = \frac{v - u}{t} \quad\text{(m/s²)}$

where u is the starting velocity and v is the velocity after time t. If a car accelerates from 5 m/s to 25 m/s in 4 s, a = (25 − 5) ÷ 4 = 5 m/s².

Acceleration can be negative — this means the object is slowing down (often called deceleration) or speeding up in the opposite direction. MYP examiners like to test whether you understand that a negative value still describes a real acceleration.

A distance-time graph plots how far an object has travelled (y-axis) against time (x-axis).

• A straight, sloping line = constant speed. The steeper the line, the faster the object.
• A horizontal (flat) line = stationary (distance is not changing).
• A curve that gets steeper = speeding up (accelerating).
• A curve that gets less steep = slowing down (decelerating).

The gradient of any straight section gives the speed for that section:

$\text{speed} = \frac{\text{rise}}{\text{run}} = \frac{\Delta\text{distance}}{\Delta\text{time}}$

In the diagram above, region A might be 60 m in 3 s = 20 m/s. Region B has zero gradient, so the object is at rest. Region C is steeper than A, so the object is moving faster.

A velocity-time graph plots velocity (y-axis) against time (x-axis). It looks similar to a distance-time graph but tells you something different.

Two key relationships:

1. Gradient = acceleration: a positive slope means speeding up, a negative slope means slowing down, and a horizontal line means constant velocity.
2. Area under the graph = distance travelled. To find the distance for a curve, break it into triangles and rectangles, then add the areas.

For the simple example above with three straight regions, the area is the trapezium shape highlighted — its area equals the total distance the object covered.

Tip: if examiners ask for displacement rather than distance, areas below the x-axis (negative velocity) count as negative and partly cancel the positive area above.

For an object moving in a straight line with constant acceleration, the following equations apply:

Symbol	Meaning	Unit
u	initial velocity	m/s
v	final velocity	m/s
a	acceleration	m/s²
s	displacement (or distance, on a straight line)	m
t	time taken	s

The three core equations of motion (often called the "suvat" equations):

$v = u + at$

$s = ut + \tfrac{1}{2}at^2$

$v^2 = u^2 + 2as$

Choose the equation that contains the three quantities you know and the one you want to find.

Worked example. A cyclist accelerates from 4 m/s to 12 m/s in 5 s along a straight path.

• Acceleration: a = (v − u) ÷ t = (12 − 4) ÷ 5 = 1.6 m/s².
• Distance covered: s = ut + ½at² = (4 × 5) + ½(1.6)(5²) = 20 + 20 = 40 m.

For free fall on Earth (no air resistance), acceleration a = g = 9.8 m/s² downwards. A dropped ball from rest after 2 s has v = 0 + 9.8 × 2 = 19.6 m/s.

MYP Sciences criteria B (Inquiring and Designing) and C (Processing and Evaluating) often involve a motion investigation. Three common methods:

1. Light gates — a beam of infrared light is broken twice by a "double interrupt card" on a moving trolley. The data logger times each break and calculates instantaneous velocity from the card length and the time gap. Two gates give acceleration.
2. Ticker timer — a tape attached to a trolley is pulled through a vibrating ticker that prints 50 dots per second. Counting dots between intervals gives distance per unit time → velocity, and changes in dot-spacing give acceleration.
3. Video analysis — record motion at a known frame rate (e.g. 30 fps) and use software (e.g. Tracker) to mark the position each frame. Distance per frame ÷ frame time = velocity.

A good investigation report follows the MYP Sciences criteria:

• Criterion B: clear research question, testable hypothesis, identified independent / dependent / controlled variables, safety considerations.
• Criterion C: organised raw data, repeated readings, mean values, suitable graph, calculated gradients with units.
• Criterion D: evaluation of accuracy, anomalous results, sources of systematic vs random error, and the wider impact (e.g. how this matters for road safety design).