Q228 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 228 (5 marks)
A 2 kg particle moves in positive x under resultant force F(x)=6x N, starting from rest at x=1 m.
a)[3 marks]
Determine its speed for .
b)[2 marks]
Find speed and acceleration at x=2 m.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) . (b) m/s; m/s squared.
Worked solution
(a) Newton gives a=3x. Use and integrate from x=1,v=0 to obtain . Choose the positive branch for positive motion.
(b) Substitution gives and a=3(2)=6. The position-dependent force cannot be treated as its initial constant value.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Part a: Convert force to acceleration.
Part a: Integrate with the initial position and speed.
Part a: Select the positive branch.
Part b: Evaluate speed.
Part b: Evaluate acceleration.
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