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You can only drop one mark across the whole paper to get 95% A1+

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1. (a) v = 6.2t + 4.1 {1} differentiate once

(b) 72 = 6.2t + 4.1 {1} sub in v=72 and solve

t = 11 s {1}

(c) a = 6.2 ms^−2 {1} differentiate again, unit!

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S=ut+1/2at^2

100=0+1/2a8^2

100+32a

a=3.1ms^-2

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distance = (1/100)*100=1%

Time = (0.4/8)*100=5%

Time^2 = 5*2 = 10%

ans = 10%

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The centripetal force required to keep the stone in place becomes too big (higher than frictional force holding the stone in place)

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F=mv^2/r

3=0.004v^2/0.3

0.9=0.004v^2

v=15ms^-1

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at a tangent to the circle, at the point that the force exceeds the radial centripetal force.

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The plane needs to be banked because it provides a centripetal force from the angle to keep it moving in a circular path. Rsin(angle)=Fc=mrw^2

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F=(mv^2)/r

F= (3x10^4 x 230^2)/2x10^3

F= 793500

F= 794000N

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L=IW

L=5.1 x 1.7

L=8.67 kgm^2 rads^-1