3.104: Acceleration a=t(t−2)a=t(t-2); velocity and displacement

0606/21/O/N/25 — Question 8 · 13 marks

(a)(i)
A particle has acceleration a=t(t−2)a=t(t-2) for t⩾0t\geqslant 0. When t=3t=3, the velocity is 66. Find vv at time tt.
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(a)(ii)
Find the time when PP is at rest.
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(a)(iii)
When t=2.5t=2.5, the displacement from OO is 44. Find the displacement when t=3t=3.
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(b)
Use calculus to find the approximate change in vv when tt increases from 2.52.5 by 0.020.02.
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