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Q8. (a) A body starts with an initial velocity of 2 ms^-1 and its acceleration is 3 + 4t ms^-2 where t is the time in seconds, from the start.

Given acceleration a = dv/dt and velocity v = ds/dt, where s is the displacement of the body in meters, from the starting point, determine EACH of following for the body:

(i) v as a function of t;         (4).

(ii) its velocity after 5 seconds;      (1)

(iii) its displacement, s, as a function of t;  (4)

(iv) its displacement after 6 seconds.        (1)

(b) Evaluate ∫₁⁴(√(x + 1/√x))dx         (6)