(a) If the position of a particle is given by x = 12t − 5t3, where t ≥ 0 is in seconds and x is in meters, when is the particle's velocity zero? (b) When is its acceleration a zero?
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(a) If the position of a particle is given by , where is in seconds and is in meters, when is the particle's velocity zero?
(b) When is its acceleration a zero?
![(a) A particle which is moving in a straight line with constant acceleration 2 m/s2 is initially at rest. Find the distance covered by the particle in the third second of its motion. [4 marks] (b) The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle. Find the velocity and acceleration of the particle when t = 3 s. [4 marks] (c) A bicycle moves along a straight road such that its position is described by the graph shown. Construct the v−t graph and a−t graph for 0 ≤ t ≤ 30 s.](https://www.doubtrix.com/uploads/editor/7222719326dsBBXaPfWp.jpg)
