(a) A particle moves on a straight path with an initial speed u and final speed v in time t. Show that the total distance X covered by the particle is given by

\(x = ut + \frac{1}{2}at^2\)

where a is the magnitude of acceleration

(b) State;

(i) Newton's second law of motion

(ii) the principle of conservation of energy

(iii) the law of floatation.

(c) Consider a balloon of mass 0.030 kg being inflated with a gas of density 0.54 kg m\(^{-3}\). What will be the volume of the balloon when it just begins to rise in air of density 1.29 kg m\(^{-3}\)? [ g = 10 ms\(^{-2}\)]

(a) State two differences between boiling and evaporation.

(b) A closed inexpansibie vessel contains air saturated with water vapour at 77°C. The total pressure in the vessel is 1007 mmHg. Calculate the new pressure in the vessel if the temperature is reduced 1.2 27°C. [ The s.v.p. of water at 77°C and 27°C respectively are 314 mmHg and 27 mmHg. Treat the air in the vessel as an ideal gas]

(c) The lengtn of a zinc rod at 23°C is 200 m. Calculate the increase in length of the rod when its temperature rises to 33°C. [ expansivity of zinc = 2.6 x 10\(^{-5}\) K\(^{-1}\)]

(d) Explain with there is no temperature change when a solid being heated changes into liquid at its melting point.

(a) The equation y = \(\alpha\) sin (wt - kx) represents a plane wave travelling in a medium along the x-direction, being the displacement at the point x at time t.

(i) Given that x is in metres and t is in seconds, state the units of k and w

(ii) What physical quantity does \(\frac{W}{k}\) represent? Justify your answer

(iii) State whether the wave is travelling in the positive or negative x-direction.

(b)(i) What are beats?

(ii) A sonometer wire has a frequency of 259 Hz. It is sounded alongside a tuning fork of frequency 256 Hz. Calculate the beat frequency

(iii) The sonometer wire in (b)(ii) above is under a tension of 1200 N. If a metre of the wire has a mass of 0.03 kg, calculate the length l of the wire when it is vibrating in the fundamental mode.

(c) List two similarities between the human eye and the photographic camera.

(a) What is a magnetic field?

(b) With the aid of a labelled diagram describe an experiment to show that a magnetic field exists around a straight wire carrying current.

(c) A 40 \(\mu\)F capacitor in series with a 40 Q resistor is connected to a 100 V, 50 Hz a.c. supply.

(i) Draw a circuit diagram of the arrangement

(ii) Calculate the: I. impedance in the circuit; II. current in the circuit III. potential difference across the capacitor.

(a)(i) State Einstein's equation of photoelectric effect

(ii) What conservation principle does the equation represent?

(b) List three applications of photocells

(c) A photo emissive surface has a threshold frequency of 4.02 x 10\(^{14}\)Hz. If the surface is illuminated by light of frequency 5.0 x 10\(^{15}\)Hz, calculate the:

(i) threshold wavelength;

(ii) work function;

(iii) kinetic energy of the emitted photoelectrons. [ c = 3.0 x 10\(^{8}\) ms\(^{-1}\), h = 6.63 x 10\(^{-34}\) Js]