Q282 · Practice questionTechnology-freeComplex familiar6 marks
QUESTION 282 (6 marks)
A delivery robot moves along a straight corridor with acceleration . At , its velocity is and its position is m from the reference point.
![Velocity graph v(t)=3t squared-4t+1 on [0,2], with two zero crossings and a negative portion between them.](/qce-data/assets/methods-2026-MM26-ORIG-044-mobile.svg)
a)[4 marks]
Determine its velocity and position functions.
b)[2 marks]
Determine the times in the first seconds when the robot changes direction.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
a) , . b) s and s.
Worked solution
a) Integrate acceleration and use to get . Integrate velocity and use to get .
b) vanishes at and . Its sign is , then , then , so both times are direction changes.
Exact answers unless rounding is specified; equivalent forms accepted.
a) Integrates acceleration.
a) Uses the initial velocity.
a) Integrates velocity.
a) Uses the initial position.
b) Determines both zero-velocity times.
b) Establishes velocity sign changes.
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