HSC Mathematics TEST
Motion in a Straight Line
NSW Syllabus Ref: 14.3
© Mathematics Plus, 2002
In Questions 1 to 4, a particle moves in a straight line from a fixed point O. The distance of the particle from O at time t seconds is given by    x = 2t3 � 6t2 + 6t + 1.

Q1.    The distance x increases for

       

Q2.    The particle's minimum speed is

  1   2   3   0

Q3.    The particle's acceleration is positive for

       

Q4.    The particle's speed decreases when its velocity and acceleration are opposite in sign.
          This occurs for

       

Q5.    The displacement from the origin of a particle moving along a straight line is given by    x = t4 � 4t3.
          The maximum displacement during the time interval     is

  27   3   12   48

In Questions 6 to 9, a particle moves from rest in a straight line. Its velocity after t seconds is given by
v = 12t2 � 18t + 6.  (v is in metres per second.)

Q6.    The particle's displacement after 2 seconds is

  8 metres   18 metres   30 metres   0 metres

Q7.    How many times does the particle reverse direction?

  4   3   2   1

Q8.    How far does the particle travel before it first reverses direction?

  1 metre   1.25 metres   1.5 metres   2 metres

Q9.    How far does the particle travel in the first second?

  1 metre   1.25 metres   1.5 metres   2 metres

Q10.    A particle P moves in a straight line. Its displacement, velocity and acceleration are given by x, v and a respectively. Which of the following statements about the particle's motion is not always true?

  If v is positive, then P is moving to the right.
  If a is positive, then v is increasing.
  P reverses direction when v is zero and a is nonzero.
  If v is positive, then the distance of P from the origin is increasing.
  If v and a are both positive or both negative, then the speed of P is increasing.
  If v and a are opposite in sign, then the speed of P is decreasing.

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