Q361 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 361 (5 marks)
Two particles move on a straight line with velocities and m/s for . They have equal velocities at .
a)[2 marks]
Determine the next time at which their velocities are equal.
b)[3 marks]
How much further does particle B travel than particle A between these two times? Justify using distances.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
a) s. b) Particle B travels m further.
Worked solution
a) Equality gives , so . The next equality is at .
b) and on , so distance equals the integral of velocity for each. The difference is .
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Solves the velocity equality.
Selects the next positive time.
Checks that both velocities are positive.
Sets up the difference of distances.
Evaluates the difference exactly.
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