Signed area and distance on a trigonometric velocity graph

Signed area and distance on a trigonometric velocity graph

Secondary 4
9 marks
TGM Original Questions

The velocity, \(v\) m/s, of a particle moving along a straight line is \(v=6\sin t-3\) for \(0\leq t\leq2\pi\), where \(t\) is in seconds. The diagram shows its velocity-time graph.

  1. Find the exact times at which the particle changes direction.[2]
  2. Find the displacement of the particle from its starting point after \(2\pi\) seconds.[2]
  3. Find the total distance travelled and the average speed over the interval. Give exact answers.[5]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \(\frac\pi6,\frac{5\pi}6\) s. (b) \(-6\pi\text{ m}\). (c) \(12\sqrt3+2\pi\text{ m}\); \(1+\frac{6\sqrt3}{\pi}\text{ m/s}\).

Need help? Join our JC Math tuition classes.

Learn more