Q222 · Practice questionTechnology-freeComplex familiar6 marks
QUESTION 222 (6 marks)
A particle has acceleration m/s squared. At x=0 it moves in the positive direction with speed 4 m/s.
a)[3 marks]
Use to determine velocity until the first turning point.
b)[3 marks]
Determine the first turning position and elapsed time.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
(a) . (b) m; s.
Worked solution
(a) Integrating gives . At x=0, v=4 gives C=8, hence . Take the positive root before the first turn.
(b) Setting v=0 gives x=. The SHM equation has solution with the given initial values. The first maximum has , giving the time.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Part a: Use acceleration in terms of position.
Part a: Integrate and apply the initial speed.
Part a: Choose the positive branch.
Part b: Find the turning position.
Part b: Obtain the SHM solution or time integral.
Part b: Find the first turning time.
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