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Question id: 79. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is allowed.
Very accurate equipment was used to measure the movement of a particle which moved in a straight line for 3 seconds. Its velocity, \(v\) ms-1 , at time \(t\) seconds, is given by:$$v=(t^2-5)^3$$
(a) Find the velocity of the particle when \(t=2\).
(b) Find the value of t for which the particle is at rest.
(c) Find the total distance the particle travels during the first three seconds.
(d) Show that the acceleration of the particle is given by \(a=6t(t^2-5)^2\)
(e) Find all possible values of t for which the velocity and acceleration are both positive or both negative.
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