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Exam-Style Questions on Velocity Time GraphProblems on Velocity Time Graph adapted from questions set in previous Mathematics exams. |
1. | IB Analysis and Approaches |
A particle moves in a straight line such that it passes through a fixed point \(O\) at time \(t = 0\), where \(t\) represents time measured in seconds after passing \(O\). For \(0 \le t \le 10\) its velocity, \(v\) metres per second, is given by:
$$v = 3\cos(0.7t) + 0.5t - 2.5$$
The graph of \(v\) is shown in the following diagram.
(a) Find the smallest value of \(t\) when the particle changes direction.
The displacement of the particle is measured in metres from \(O\).
(b) Find the range of values of \(t\) for which the displacement of the particle is increasing.
(c) Find the displacement of the particle relative to \(O\) when \(t = 10\).
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