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Cambridge IGCSE Physics · 0625

Chapter 1: Motion, forces and energy — Part 2

Topic 1.2 · Motion

Speed and average speed

Speed is distance travelled per unit time.

v = s / t where v is speed in m/s, s is distance in m, and t is time in s.

Average speed = total distance travelled / total time taken. Use this when speed is not constant for the whole journey.

A cyclist travels 1.2 km in 2.5 minutes. Calculate her average speed in m/s.

Worked example: convert 1.2 km and 2.5 minutes to SI units, then speed is 8.0 metres per second
Convert first (1200 m, 150 s), then v = s / t = 8.0 m/s.

Velocity is speed in a given direction. A car going around a roundabout at constant speed still has a changing velocity because direction changes.

Distance–time and speed–time graphs

You must sketch, plot and interpret both types of graph.

Distance–time: at rest
Horizontal line — distance does not change.
Distance–time: constant speed
Straight line with constant gradient. Speed = gradient = Δs / Δt.
Distance–time: accelerating
Curve with increasing gradient (steeper).
Distance–time: decelerating
Curve with decreasing gradient (flattening).
Speed–time: constant speed
Horizontal line.
Speed–time: constant acceleration
Straight line with constant gradient.
Speed–time: changing acceleration
A curve (gradient is not constant).

On a speed–time graph, distance travelled is the area under the line for constant speed or constant acceleration (triangles, rectangles and trapezia).

A scooter accelerates uniformly from rest to 12 m/s in 5.0 s, then travels at 12 m/s for a further 10 s. Calculate the distance travelled in the 15 s.

Worked example: distance is area under a speed-time graph, triangle 30 m plus rectangle 120 m equals 150 m
Area = triangle + rectangle = 30 m + 120 m = 150 m.
Distance–time graphs: horizontal line (at rest), straight line with constant positive gradient (constant speed), and a curve with increasing gradient (accelerating).
Diagram 1: Distance–time graphs: horizontal line (at rest), straight line with constant positive gradient (constant speed), and a curve with increasing gradient (accelerating).
Speed–time graphs: horizontal line (constant speed), sloping straight line (constant acceleration), and a curve (changing acceleration), with the area under the line shaded as distance travelled.
Diagram 2: Speed–time graphs: horizontal line (constant speed), sloping straight line (constant acceleration), and a curve (changing acceleration), with the area under the line shaded as distance travelled.

Exam Traps

  • Do not read speed from the height of a distance–time graph — speed is the gradient. Area under a distance–time graph is not distance; that rule is for speed–time graphs.

Acceleration of free fall

Near the Earth’s surface the acceleration of free fall g is approximately constant and approximately 9.8 m/s2.

With no air or liquid resistance, a falling object’s speed increases steadily (constant acceleration g).

Acceleration

Acceleration is change in velocity per unit time.

a = Δv / Δt   Unit: m/s2.

On a speed–time graph, acceleration is the gradient.

A deceleration is a negative acceleration. Use a negative sign in calculations when velocity is decreasing in the chosen positive direction.

A car speeds up from 8.0 m/s to 20 m/s in 4.0 s. Calculate its acceleration.

Worked example: acceleration is change in velocity over time, 3.0 metres per second squared
a = (20 − 8.0) / 4.0 = 3.0 m/s2.

Falling with air or liquid resistance

In a uniform gravitational field with air or liquid resistance (drag):

  • Weight acts downwards and is constant (for a given mass).
  • Drag increases as speed increases and acts upwards.
  • Resultant force = weight − drag, so acceleration decreases as the object speeds up.
  • When drag = weight, resultant force is zero and the object falls at a constant terminal velocity.
Object falling in a uniform gravitational field: (left) no air resistance, speed increasing linearly; (right) with air resistance, speed rising then levelling at terminal velocity when drag equals weight.
Diagram 3: Object falling in a uniform gravitational field: (left) no air resistance, speed increasing linearly; (right) with air resistance, speed rising then levelling at terminal velocity when drag equals weight.

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