A Level Physics 9702 Paper 22, May/June 2025

Table 1.1 lists some physical quantities. Identify with ticks (✓) which quantities are vectors and which are scalars. Table 1.1

A constant resultant force $F$ acts on a car of mass $m$. The car moves from rest with constant acceleration $a$ along horizontal ground. When the car has displacement $s$, the speed of the car is $v$. Using the concept of work done on the car, show that the kinetic energy $E_{\mathrm{K}}$ of the car is given by the equation $$E_{\mathrm{K}}=\frac{1}{2}m{v}^2\mathrm{.}$$

The mass of the car is $920\text{ kg}$. At time $t=0$, the car is at rest. At time $t=5.8\text{ s}$, its velocity is $17\text{ m}{\text{s}}^{-1}$. Calculate the kinetic energy of the car at time $t=5.8\text{ s}$. kinetic energy = ....................................................... J

Between time $t=0$ and time $t=5.8\text{ s}$, the work done against resistive forces is $4.7\times {10}^4\text{ J}$. Determine the average output power of the car during this time. power = ..................................................... W

At time $t=5.8\text{ s}$, the speed of the car becomes constant. State and explain whether the output power of the car is greater than, less than or the same as the output power just before $t=5.8\text{ s}$.

Define the moment of a force about a point.

A tree of mass $270\text{ kg}$ grows out of sloping ground and is supported by a post, as shown in Fig. 2.1. The ground applies a total force $R$ on the tree at point Q. The centre of gravity of the tree is a horizontal distance of $1.2\text{ m}$ from Q. The post applies a force $F$ of $1800\text{ N}$ perpendicular to the line PQ. The line of action of $F$ passes through point P at an angle $\theta$ to the vertical. P is a horizontal distance of $1.6\text{ m}$ from Q. The tree is in equilibrium and all forces act on the tree in the same plane. By taking moments about point Q, show that $\theta$ is ${25}^{\circ }$.

On Fig. 2.2, draw a labelled scale vector triangle to represent the forces acting on the tree. The weight of the tree has been drawn to scale.

The tree exerts a pressure of $150\text{ kPa}$ on the top of the post. Determine the surface area of the tree in contact with the post. area = .................................................... ${\text{m}}^2$

State the amplitude of wave X. amplitude = ................................................... cm

Both waves have frequency $16\text{ Hz}$. Determine the speed of wave X. speed = ................................................ $\text{m}{\text{s}}^{-1}$

State and explain whether X and Y are coherent.

Wave X and wave Y superpose to form a resultant wave. On Fig. 3.2, sketch the variation of displacement of the resultant wave with distance from A at the instant of time shown in Fig. 3.1.

The intensity of wave X is $I_{\mathrm{X}}$. The intensity of wave Y is $I_{\mathrm{Y}}$. Use Fig. 3.1 to determine the ratio $\frac{I_{\mathrm{X}}}{I_{\mathrm{Y}}}$. ratio = .........................................................

State and explain whether the collision is elastic or inelastic.

Calculate the change in momentum of the ball during the collision with the ground. change in momentum = ............................................ $\text{kg}\text{m}{\text{s}}^{-1}$

Determine the average force on the ball during the collision with the ground. force = ...................................................... N

Calculate the ratio $\frac{h_2}{h_1}$. ratio = .........................................................

Define the Young modulus.

A wire of unstretched length $0.81\text{ m}$ is made of a metal with Young modulus $95\text{ GPa}$. The wire obeys Hooke’s law and has a constant cross-sectional area. Fig. 5.1 shows the force–extension graph for the wire. Determine the cross-sectional area of the wire. area = .................................................... ${\text{m}}^2$

The extension of the wire is initially $2.0\times {10}^{-3}\text{ m}$. Determine the work done to increase the extension of the wire to $3.0\times {10}^{-3}\text{ m}$. work done = ....................................................... J

Define electric potential difference across a component.

A circuit contains four resistors and a battery of electromotive force (e.m.f.) $8.0\text{ V}$ with negligible internal resistance. When the variable resistor has resistance $R$, the currents in the circuit are $0.030\text{ A}$, $I_1$ and $I_2$, as shown in Fig. 6.1. Determine the charge passing through the battery in a time of $4.0\text{ minutes}$. charge = ...................................................... C

Calculate $I_1$. $I_1$ = ...................................................... A

Calculate $I_2$. $I_2$ = ...................................................... A

Determine $R$. $R$ = ...................................................... $\mathrm{\Omega }$

The variable resistor in (b) is fitted with a scale so that its resistance can be accurately determined. The resistor of resistance $240\mathrm{\Omega }$ is now replaced by a new resistor X of unknown resistance. A galvanometer is connected as shown in Fig. 6.2. With reference to ratios of resistances, explain how this circuit can be used to determine the resistance of X.

State what is meant by a fundamental particle.

A nucleus X has 14 nucleons and $p$ protons. The ratio of charge to mass for nucleus X is $4.1\times {10}^7\text{ C}{\text{kg}}^{-1}$. Determine $p$. $p$ = .........................................................

Nucleus X undergoes ${\beta }^{-}$ decay to form nucleus Z. Complete the equation representing this decay. $${}_{\dots \dots }^{14}\text{X}\to {}_{\dots \dots }^{\dots \dots }\text{Z}+{}_{\dots \dots }^{\dots \dots }\dots \dots +{}_{\dots \dots }^{\dots \dots }\dots \dots$$

A sample of a radioactive substance emits particles that are positively charged and have a continuous range of kinetic energies. State and explain whether the nuclei in the sample are undergoing $\alpha$-decay, ${\beta }^{+}$ decay or ${\beta }^{-}$ decay.