(Solved): The motorboat shown in figure 3 below travels from rest around a circular path of radius of curvat ...

The motorboat shown in figure 3 below travels from rest around a circular path of radius of curvature \( =50 \mathrm{~m} \) at a speed that increases with time, \( v=\left(0.2 \mathrm{t}^{2}\right) \mathrm{m} / \mathrm{s} \). Find the following at an instant \( t=3 s \) : 3.1 the normal acceleration; 3.2 the tangential acceleration; 3.3 magnitude of the total acceleration of the motorboat. \( 3.4 \) If the path is changed to the one described by the equation \( y=0.36 x^{2} \), what is percentage change in the radius of curvature at distance of \( 4 \mathrm{~m} \) in the \( \mathrm{x} \)-direction compared to the circular path. Figure 3