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Cambridge IGCSE0625

Motion

Physics 0625 Chapter Notes

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Motion
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In this chapter

  1. 1Speed, velocity and average speed
  2. 2Reading distance–time and speed–time graphs
  3. 3Speed from a distance–time graph
  4. 4Distance from a speed–time graph
  5. 5Acceleration of free fall
  6. 6Acceleration
  7. 7Constant and changing acceleration
  8. 8Falling with and without resistance

1. Speed, velocity and average speed

Speed is distance travelled per unit time. Velocity is speed in a given direction.

For a whole journey, average speed is total distance divided by total time.

v = s/t

average speed = (total distance travelled)/(total time taken)

Examiner insight

“Some candidates confused maximum speed with average speed for the whole journey.”

Worked example 14 marks

A student runs a distance of 400 m in a time of 2.0 minutes. Calculate the average speed of the student. Give your answer in m / s.

  1. 1

    average speed = total distance ÷ time taken [1]

  2. 2

    time = 2 × 60 = 120 s [1]

  3. 3

    average speed = 400 ÷ 120 [1]

  4. 4

    = 3.3 m/s [1]

2. Reading distance–time and speed–time graphs

On a speed–time graph, a rising line means the speed is increasing, a horizontal line means constant speed, and a falling line means the speed is decreasing.

On a distance–time graph, a horizontal line means the object is at rest. A line getting steeper means it is accelerating, and a line getting less steep means it is decelerating.

Examiner insight

“Some candidates confused the regions of the speed-time graph with those of a distance-time graph.” “Weaker candidates gave vague answers of ‘constant’, ‘constant motion’, ‘no acceleration’ or an incorrect answer of ‘stationary’.”

3. Speed from a distance–time graph

Speed is the gradient of a straight-line section of a distance–time graph. The maximum speed is where the gradient is steepest.

speed = gradient = (change in distance)/(change in time)

Examiner insight

“Candidates recognised that the maximum speed is shown by the steepest gradient on the distance-time graph.” “A few candidates mistook the graph for a speed-time graph, giving a pair of points for each answer.”

Worked example 13 marks

A student cycles from home to school. The graph shows the distance–time graph for this journey. Use the graph to calculate the student's maximum speed in km / h.

  1. 1

    speed = gradient of the distance–time graph [1]

  2. 2

    speed = (1.25 - 0.4)/(7.5 - 5.0) = 0.34 km/min [1]

  3. 3

    convert min to h: 0.34 × 60 = 20 km/h [1]

4. Distance from a speed–time graph

Distance travelled is the area under the speed–time graph, for the time interval the question gives. Under a horizontal line it is base × height. Under a sloping line from zero it is ½ × base × height.

Examiner insight

“Weaker candidates attempted to use s = vt instead of the area under the graph.” “The most common errors were calculations of the area underneath the whole graph, misreading the speed axis or omitting or giving an incorrect unit.”

Worked example 13 marks

The graph shows the speed–time graph for a person skiing. Calculate the distance travelled between time = 0 and time = 4.0 s by the person skiing.

  1. 1

    distance travelled = area under graph [1]

  2. 2

    = 1/2 × 4.0 × 8.0 [1]

  3. 3

    = 16 m [1]

5. Acceleration of free fall

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

Examiner insight

“A significant number of weaker candidates had the misconception that the ball would fall with increasing acceleration.”

Worked example 11 mark

A falling object near to the surface of the Earth has an acceleration of free fall g. What is the approximate value of g, and what is the approximate change in g as the object gets nearer to the Earth?

A 8.9 m / s², decreases · B 8.9 m / s², no change · C 9.8 m / s², decreases · D 9.8 m / s², no change

  1. 1

    D: 9.8 m / s², no change. [1]

6. Acceleration

Acceleration is change in velocity per unit time. On a speed–time graph it is the gradient.

A deceleration is a negative acceleration.

a = (Δ v)/(Δ t)

Examiner insight

“Candidates should remember that acceleration can be expressed as the rate of change in velocity or the change in velocity per unit time.” “Common errors included the calculation of 1 ÷ gradient, the use of a single point on the graph or an attempt to use equations to calculate the value of the acceleration.”

Worked example 12 marks

The graph shows a speed–time graph for a toy aircraft. Calculate the acceleration between time = 0 and time = 18 s.

  1. 1

    a = (Δ v)/(Δt) = 45/18 [1]

  2. 2

    = 2.5 m/s² [1]

7. Constant and changing acceleration

On a speed–time graph, a straight sloping line means constant acceleration: the gradient stays the same. A curved line means changing acceleration.

Examiner insight

“Two common correct answers were that the gradient remains constant, or that the line does not curve.”

8. Falling with and without resistance

Without air resistance, an object falls with constant acceleration.

With air or liquid resistance, the resistance increases as the speed increases. When the resistance equals the weight, the resultant force is zero and the object falls at a constant speed: its terminal velocity.

Examiner insight

“Few candidates stated that air resistance increases as velocity increases, and many linked the increase in air resistance with time.” “Terminal velocity occurs when the drag forces are equal to the downward force of weight and therefore the resultant force on the object is zero and it travels at a constant speed.”

Recap

  • Speed = distance per unit time. Velocity = speed in a given direction.
  • Average speed = total distance ÷ total time.
  • Distance–time graph: gradient = speed, horizontal = at rest.
  • Speed–time graph: area under it = distance, horizontal = constant speed.
  • g is approximately 9.8 m/s² near the Earth's surface.
  • Extended: acceleration = change in velocity per unit time = gradient of a speed–time graph.
  • Extended: at terminal velocity, resistance equals weight and the resultant force is zero.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. State how velocity is different from speed.1 mark
  2. A cyclist travels 3.6 km in 12 minutes. Calculate her speed in m / s.3 marks
  3. A runner covers the first 400 m of a race in 80 s and the next 400 m in 120 s. Calculate his average speed for the whole race.3 marks
  4. The graphs show the motion of two objects, A and B. Describe the motion of each object between 10 s and 30 s.2 marks
  5. The graph shows the distance–time graph for part of a journey. Calculate the speed of the object between 20 s and 50 s.3 marks
  6. The graph shows the speed–time graph for an object. Calculate the total distance travelled in the 16 s shown.4 marks
  7. A ball is dropped from a tall building. Air resistance is negligible. State the acceleration of the ball 1 s after release and 3 s after release.2 marks
  8. A car slows from 30 m / s to 12 m / s in 4.0 s. Calculate its acceleration.3 marks
  9. The graph shows the speed–time graph for a car. (a) State how the graph shows that the acceleration is constant. (b) Calculate the acceleration.3 marks
  10. A skydiver jumps from an aircraft. Describe and explain how her speed and acceleration change from the moment she jumps until she reaches terminal velocity.5 marks

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