A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t3 − 6t2 + 9t − 2, 0 ≤ t ≤ 7. Find the total distance the particle travels in 7 units of time. units
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A particle is moving along the -axis. The position of the particle at time is given by . Find the total distance the particle travels in 7 units of time.
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![(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)
