1.40: A particle is moving along a straight line.

4PM1/1/November/2024 — Question 5 · 10 marks

A particle P\displaystyle P is moving along a straight line.
At time t\displaystyle t seconds (t≥0\displaystyle t \geq 0), the velocity, v\displaystyle vm/s\displaystyle \mathrm{m}/\mathrm{s}, of P\displaystyle P is given by
v=3t2−16t+5v = 3t^2 - 16t + 5
(a) Find the values of t\displaystyle t when P\displaystyle P is instantaneously at rest.
(3)
At time t\displaystyle t seconds the acceleration of P\displaystyle P is a\displaystyle am/s2\displaystyle \mathrm{m}/\mathrm{s}^{2}
(b) Find the range of values of t\displaystyle t for which a>0\displaystyle a > 0
(2)
(c) Find the distance, in m, that P\displaystyle P travels in the interval 1≤t≤4\displaystyle 1 \leq t \leq 4
(5)