Determine displacement given velocity and the initial value of displacement.

A particle moves along a straight line with velocity \( v(t) = 6t - 4 \) m/s, where \( t \) is the time in seconds. At \( t = 0 \), the displacement of the particle is 3 m. State the expression for the displacement \( s(t) \) of the particle at time \( t \).

A particle moves along a straight horizontal line. Its velocity at time \( t \) seconds is given by \( v(t) = 4\sin(3t) + 1.5 \), where \( t \geq 0 \) and velocity is measured in \( \text{m s}^{-1} \). At \( t = 0 \), the particle is \( 8.0 \) m to the right of the origin. (a) Determine the displacement function \( s(t) \). [2 marks] (b) Determine the position of the particle relative to the origin when \( t = 2 \) seconds, correct to two decimal places. [2 marks]