1.34: A particle is moving along the -axis.

4PM1/1/June/2024 — Question 5 · 9 marks

A particle P\displaystyle P is moving along the x\displaystyle x-axis.
At time t\displaystyle t seconds (t≥0\displaystyle t \geq 0) the acceleration, a\displaystyle am/s2\displaystyle \mathrm{m}/\mathrm{s}^{2}, of P\displaystyle P is given by a=3t−4\displaystyle a = 3t - 4
When t=0\displaystyle t = 0, P\displaystyle P is at rest.
(a) Find the velocity of P\displaystyle P when t=4\displaystyle t = 4
(3)
At time T\displaystyle T seconds, T>0\displaystyle T > 0, P\displaystyle P is instantaneously at rest.
(b) Find the value of T\displaystyle T
(2)
When t=0\displaystyle t = 0, P\displaystyle P is at the point with coordinates (−10,0)\displaystyle (-10, 0)
(c) Find the displacement of P\displaystyle P from the origin when t=3\displaystyle t = 3
(4)