(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\(^{-2}\)]