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CIE iGCSE Co-Ordinated Science P1.5.1 Effects of forces Exam Style Questions Paper 4

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Question

(a) A rocket travels vertically upwards. Fig. 10.1 shows the speed-time graph for the rocket.
(i) Describe the motion of the rocket in the first 20 seconds.
(ii) Calculate the deceleration of the rocket between time \(= 20\text{ s}\) and time \(= 50\text{ s}\). State the unit of your answer.
(iii) Calculate the distance travelled by the rocket between time \(= 30\text{ s}\) and time \(= 50\text{ s}\).
(iv) State the time at which the rocket reaches its maximum height above the ground.
(b) A car travels at constant speed on a horizontal road.
State and describe the horizontal forces acting on the car.

Topic codes:

• Topic P1.2 — Motion / Speed-time graphs (Part (a))
• Topic P1.5.1 — Effects of forces / Balanced forces (Part (b))

▶️ Answer/Explanation

(a)(i) In the first 20 seconds, the rocket is accelerating with changing acceleration (the gradient of the speed-time graph is increasing, so the rate of change of speed is not constant).

(a)(ii) Deceleration = change in speed ÷ time

At \(t = 20\text{ s}\), speed = 400 m/s; at \(t = 50\text{ s}\), speed = 100 m/s
Change in speed = 400 − 100 = 300 m/s
Time interval = 50 − 20 = 30 s
Deceleration = 300 ÷ 30 = 10 m/s²

(a)(iii) Distance travelled = area under the graph between \(t = 30\text{ s}\) and \(t = 50\text{ s}\)

Area = \(\frac{1}{2} \times 20 \times 200 = 2000\text{ m}\)

distance = 2000 m

(a)(iv) The rocket reaches its maximum height when its speed becomes zero, at 50 s.

(b) The horizontal forces acting on the car are:

  • Driving force (from the engine, pushing the car forward)
  • Drag / air resistance / friction (opposing the motion)

Since the car travels at constant speed, these forces are equal in magnitude and opposite in direction — the resultant force is zero.

Question

A student investigates a spring.
The student adds slotted masses to the spring to increase the force applied to the spring as shown in Fig. 3.1.
(a) The student records the length of the spring as it extends. Fig. 3.2 shows the results obtained by the student.
(i) Use Fig. 3.2 to determine the original length of the spring.
(ii) Use Fig. 3.2 to calculate the spring constant of the spring.
(iii) State the term used to describe point X on the graph.
(b) The slotted masses used by the student are made from steel.
Fig. 3.3 shows one of the slotted masses
Describe how the student determines the density of the steel used to make the slotted masses.
measurement 1 ___________
measurement 2 ___________
calculation ___________
(c) Fig. 3.4 shows how a long spring can be used to demonstrate wave motion.
(i) On Fig. 3.4 use a double headed arrow (\(\updownarrow\) or \(\leftrightarrow\)) to label the amplitude of the wave.
(ii) The wave shown in Fig. 3.4 is a transverse wave. Complete the sentence to describe the properties of a transverse wave.
Transverse waves are made by oscillations which act ___________ to the direction of energy transfer.

Most-appropriate topic codes (Cambridge IGCSE Co-ordinated Sciences 0654, 2025–2027 syllabus):

• Topic P1.5.1 — Effects of forces (Part (a))
• Topic P1.4 — Density (Part (b))
• Topic P3.1 — General properties of waves (Part (c))

▶️ Answer/Explanation

(a)(i)

The original (unloaded) length of the spring is read from where the graph line meets the y-axis (zero force).
Original length = 2.0 cm.
This is the length of the spring before any force is applied.

(a)(ii)

From the linear portion of the graph, using \( F = k \times x \) where \(x\) = extension (not total length).
Taking two points on the straight line, e.g. at \(F = 0\text{ N}\), length = 2.0 cm and at \(F = 5.0\text{ N}\), length = 12.0 cm, so extension = 10.0 cm.
Spring constant \( k = \frac{F}{x} = \frac{5.0}{10.0} = \mathbf{0.5} \) N/cm.

(a)(iii)

Point X is called the limit of proportionality.
Beyond this point, the extension is no longer proportional to the applied force (Hooke’s Law no longer applies).
The spring may become permanently deformed if stretched beyond the elastic limit.

(b)

Measurement 1: Measure the volume of the slotted mass using a displacement method (e.g. submerge it in a measuring cylinder or eureka can and record the volume of water displaced).
Measurement 2: Measure the mass of the slotted mass using a balance/scales.
Calculation: Calculate density using \( \rho = \frac{m}{V} \) (density = mass ÷ volume).

(c)(i)

The amplitude should be marked with a double-headed vertical arrow (\(\updownarrow\)) from the equilibrium (rest) position to the peak (crest) or trough of the wave.
Amplitude is the maximum displacement of a point on the wave from its equilibrium position.
It must be drawn from the centre dashed line to either the top or bottom of the wave.

(c)(ii)

Transverse waves are made by oscillations which act perpendicular / at right angles / 90° to the direction of energy transfer.
In the spring demonstration, the coils move up and down while the wave energy travels horizontally along the spring.
Examples of transverse waves include light waves and water waves.

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