(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\(^{-2}\)]
Explanation
a) Average velocity = \(\frac{u + u}{2}\) From equation V = u + at Aeverage velocity = \(\frac{u + u + at}{2}\) = \(u + \frac{1}{2} at\) Distance covered = Ave. vel. x time x = (u + \(\frac{1}{2}\)at)t x = ut +s (b)i) Newton's second law of motion states that the of change of momentum is proportional to the lied force and takes place in tho direction of the force. (ii) The principle of conservation of energy es that energy is neither created nor destroyed can be changed from one form to another. The law of floatation states that an object wil t in a fluid when the upthrust exerted upon it by fluid in which it floats equals the weight of the (c) Mass of air displaced = mass of ballon on and contents V x density of A air = V x density of gas + content V x 1.29 = v x 0.54 + 0.030 V = \(\frac{0.03}{0.75}\) = 0.04m\(^3}\)
