14. (a) State Newton's second law of motion and show that the first law of motion can be mathematically stated from the mathematical expression for the second law of motion. (b) A stone dropped from a window reaches the ground in 0.5 seconds (given g = 10 ms^-2 ).
i) calculate the speed just before it hits the ground
ii) what is average speed t = 0.5 s ?
iii) calculate the height of window from the ground
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Answer:(a)We know momentum p=mv where m= mass and v=velocity,So rate of change of momentum Δp=mv−mu where v and u are the final and initial velocity.So rate of change of momentum= tm(v−u) --------(A)Also we know acceleration a= tv−u Again ForceF=maThus A can be written as Fα tm(v−u) F=kma where k= proportionality constant.Hence from second law of motion we get force is the product of mass and acceleration.F=ma(b)(I)4.9m/s(ii)2.45m/s(iii)1.225m
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