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Further Mathematics Paper 2, Nov/Dec. 2007  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
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Question 16

(a) A particle initially at rest moves in a straight line with an acceleration of (5t – 2t2) ms-2.  Find the
(i) velocity of the particle after t seconds;
(ii) average acceleration of the particle during the 3rd second.

(b) A body of mass 25 kg, places on top of a smooth plane inclined at an angle of 60° to the horizontal, slides down.  If the plane is 250 metres long, calculate, correct to one decimal place, the
(i) time taken to reach the ground;
(ii) speed with which it touches the ground
[ Take g = 10 m-2]

_____________________________________________________________________________________________________
Observation

Most candidates found it difficult to interprete the question correctly. Most candidates could not calculate the average acceleration of the particle during the third second correctly. More succinctly, instead of integrating the given acceleration before substituting the time of the 3rd and 2nd seconds, most candidates substituted the times directly in the given acceleration.  This led to the wrong solution by most candidates.

In the (b) part, the component of the acceleration along the place would be
gsinθ = 10sin60 =   5√3  m/s2.  
Using S = ut + ½ at2, u = o, »  250  =  ½ (5√3)t2  » t   =  7.6s

(ii)  Using v = u + at, u = 0, a = 5√3,  t = 7.6  » v = 5√3(7.6) = 65.8 ms-1

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