subunit (b) Movement and position

What is distance?

The total length of the path travelled by an object (a scalar quantity – it has no direction).

What is displacement?

The straight-line distance from the starting point to the finishing point, in a specified direction (a vector quantity – it has both magnitude and direction).

What is speed?

The rate of change of distance. How quickly an object is moving.

What are the axes on a distance-time graph?

X-axis: Time (in seconds, s). Y-axis: Distance (in metres, m).

What does the slope (gradient) of a distance-time graph tell you?

The speed of the object. A steeper slope means a higher speed.

What does a straight diagonal line upwards on a distance-time graph mean?

The object is moving at a constant speed.

What does a curved line getting steeper on a distance-time graph mean?

The object is accelerating (speeding up). Its speed is increasing.

What does a curved line getting less steep on a distance-time graph mean?

The object is decelerating (slowing down). Its speed is decreasing.

What does a horizontal straight line on a distance-time graph mean?

The object is stationary (at rest). Speed = 0 m/s.

What does a line going downwards on a distance-time graph mean?

The object is moving back towards the start (decreasing distance from the origin). Speed is still positive, but the object is moving in the opposite direction.

How do you calculate speed from a distance-time graph for a straight line?

Speed = Gradient of the line. Choose two points on the line and calculate (y₂

How do you find the speed at a specific instant on a curved distance-time graph?

Draw a tangent to the curve at that point and find the gradient of the tangent.

What is the area under a distance-time graph equal to?

It has no physical meaning in IGCSE Physics. Do not calculate it.

What is a common exam mistake when plotting distance-time graphs?

Drawing a "dot-to-dot" ruler line if the points are not perfectly in a straight line. Join points with a smooth straight line or smooth curve.

What is a common exam mistake regarding distance-time graphs?

Confusing distance-time graphs with velocity-time graphs. In a distance-time graph, a horizontal line means stationary. In a velocity-time graph, a horizontal line means constant velocity.

What is average speed?

The total distance travelled divided by the total time taken. It does not tell you the speed at any particular moment.

What is the equation for average speed?

Average Speed = Total Distance Moved / Time Taken, or v = d / t.

How do you find distance from speed and time?

d = v × t.

How do you find time from speed and distance?

t = d / v.

What is a common exam mistake when using the speed equation?

Not converting time into seconds. If a question gives time in minutes, multiply by 60. If in hours, multiply by 3600.

What is a common exam mistake regarding average speed?

Forgetting that the equation gives average speed. If an object speeds up and slows down, the instantaneous speed at any point will be different from the average speed.

What apparatus is used to measure the speed of a toy car?

Ticker-timer and ticker-tape, or light gates connected to a data logger/timer, and a metre ruler.

How does a ticker-timer work?

It makes 50 dots per second (every 0.02 seconds) on a tape as the car pulls it through. The distance between dots gives speed.

How do you find speed using a ticker-timer?

Measure the distance between two dots that are a certain number of intervals apart. Time = number of intervals × 0.02 s. Then use v = d/t.

How do you find acceleration using a ticker-timer?

Measure the length of a 5-dot section near the start (initial speed, u) and a 5-dot section near the end (final speed, v). Calculate the time between midpoints, then use a = (v

How do light gates work to measure speed?

As the object passes through the first light gate, it breaks the beam and starts the timer. When it passes through the second gate, it breaks the beam and stops the timer. Speed = distance between gates / time.

How can you increase accuracy when using light gates?

Repeat the experiment several times and calculate an average time. This reduces the effect of random errors.

Why are light gates more accurate than stopwatches?

Light gates measure time electronically with a data logger, eliminating human reaction time error.

What is a fiducial marker?

A reference point on the object used to start and stop the timer at the same point to reduce parallax error.

What is a common exam mistake regarding repeating readings?

Stating that repeating readings "makes the experiment more accurate." In IGCSE, repeating readings makes the experiment more reliable (identify anomalies and calculate a mean). Accuracy depends on equipment and method.

What is acceleration?

The rate of change of velocity. It tells you how quickly an object's velocity is increasing or decreasing.

What is deceleration?

When an object slows down, its acceleration is negative. The value of a will be a negative number.

What is the equation for acceleration?

Acceleration = Change in Velocity / Time Taken, or a = (v

What are the units for acceleration?

m/s² (metres per second squared).

How do you find final velocity from acceleration?

v = u + at.

How do you find initial velocity from acceleration?

u = v

How do you find time from acceleration?

t = (v

What is a common exam mistake in acceleration calculations?

Using v instead of (v

What is a common exam mistake regarding deceleration?

Forgetting the negative sign for deceleration. The sign is crucial in multi-step questions.

What is a common exam mistake regarding units in acceleration calculations?

Not converting time into seconds or velocity into m/s. You cannot use km/h with seconds – convert everything to SI units.

What is a common exam mistake confusing acceleration with velocity?

A high speed does not mean a high acceleration. Acceleration is the rate of change of velocity, not the velocity itself.

How can you find distance travelled during constant acceleration?

Use average speed = (v + u) / 2, then distance = average speed × time.

What is the equation for distance during constant acceleration?

d = ((v + u) / 2) × t.

What is velocity?

Speed in a given direction (a vector quantity).

What does the gradient of a velocity-time graph tell you?

The acceleration.

What does the area under a velocity-time graph tell you?

The distance travelled.

What are the axes on a velocity-time graph?

X-axis: Time (in seconds, s). Y-axis: Velocity (in metres per second, m/s).

What does a horizontal straight line on a velocity-time graph mean?

The object is moving at a constant velocity (steady speed in a straight line). Acceleration is zero.

What does a straight diagonal line upwards on a velocity-time graph mean?

The object is accelerating at a constant rate (uniform acceleration).

What does a straight diagonal line downwards on a velocity-time graph mean?

The object is decelerating at a constant rate (uniform deceleration).

What does a curved line getting steeper on a velocity-time graph mean?

The object is accelerating at an increasing rate (non-uniform acceleration).

What does a line at zero velocity (on the x-axis) on a velocity-time graph mean?

The object is stationary (at rest).

What is a common exam mistake regarding velocity-time graphs?

Confusing distance-time graphs with velocity-time graphs. In a distance-time graph, a horizontal line means stationary. In a velocity-time graph, a horizontal line means constant velocity.

What is a common exam mistake regarding the area under a velocity-time graph?

Forgetting that the area gives distance, not displacement (unless the object moves in a straight line without changing direction).

What is a common exam mistake regarding a horizontal line on a velocity-time graph?

Thinking it means the object is stationary. It means the object is moving at a constant velocity – it is only stationary if the line is on the x-axis (velocity = 0 m/s).

How do you calculate acceleration from a velocity-time graph?

Acceleration = Gradient = Change in Velocity / Change in Time = (v

What are the steps to find the gradient of a velocity-time graph?

Choose two points on the line (far apart). Calculate change in velocity (Δv) and change in time (Δt). Divide: a = Δv / Δt.

What is a common exam mistake when calculating acceleration from a graph?

Forgetting to include the units (m/s²) when calculating the gradient.

What is a common exam mistake when choosing points on a graph?

Choosing points that are too close together, leading to an inaccurate gradient. Always choose points far apart.

What is a common exam mistake regarding deceleration on a graph?

Forgetting the negative sign for deceleration.

What is a common exam mistake regarding axis values on a graph?

Using the wrong axis values (e.g., reading distance instead of velocity). Always check that you are using the y-axis (velocity) for the change in velocity.

How do you calculate distance from a velocity-time graph for a rectangle (constant velocity)?

Distance = v × t (area of rectangle = base × height).

How do you calculate distance from a velocity-time graph for a triangle (uniform acceleration from rest)?

Distance = ½ × v × t (area of triangle = ½ × base × height).

How do you calculate distance from a velocity-time graph for a trapezium (uniform acceleration with initial velocity > 0)?

Distance = ½ × (u + v) × t (area of trapezium).

What is a common exam mistake when calculating area under a velocity-time graph?

Calculating the area of a triangle when the object started with an initial velocity > 0 (it should be a trapezium). Always check the starting velocity.

How do you calculate distance for a curved velocity-time graph?

Count the number of squares under the curve. Estimate partial squares. Multiply total squares by the area of one square (time per square × velocity per square).

What is a common exam mistake regarding units for distance from a graph?

Forgetting to include the units (m) when stating the distance.

What is the equation v² = u² + 2as used for?

To find final velocity, initial velocity, acceleration, or displacement when time is NOT given.

What does s represent in v² = u² + 2as?

Displacement (the straight-line distance from start to finish, in a specified direction).

When should you use v² = u² + 2as?

When time (t) is NOT given in the question and you are NOT asked to find it.

How do you rearrange v² = u² + 2as to find final velocity?

v = √(u² + 2as).

How do you rearrange v² = u² + 2as to find acceleration?

a = (v²

How do you rearrange v² = u² + 2as to find displacement?

s = (v²

What is a common exam mistake when using v² = u² + 2as?

Forgetting to take the square root at the end. You must take the square root to find v.

What is a common exam mistake regarding deceleration in v² = u² + 2as?

Forgetting the negative sign for deceleration. If the object is slowing down, a is negative.

What is a common exam mistake regarding when to use v² = u² + 2as?

Using this equation when time is given or asked for. If time is involved, use a = (v

What is a common exam mistake regarding s in v² = u² + 2as?

Forgetting that s is displacement, not distance. If the object changes direction, s is the straight-line distance from start to finish, not the total path length.

What is a common exam mistake confusing v² = u² + 2as with another equation?

Confusing v² = u² + 2as with v = u + at. Remember: v² = u² + 2as is for when time is NOT given. v = u + at is for when time IS given.

What is the equation for average speed?

v = d / t.

What is the equation for acceleration?

a = (v

What is the equation for motion when time is NOT given?

v² = u² + 2as.

How do you find distance from a velocity-time graph?

Area under the graph (rectangle, triangle, or trapezium).

How do you find acceleration from a velocity-time graph?

Gradient of the graph.

How do you combine a = (v

u) / t and v² = u² + 2as in an exam question?