(Solved): In a particular Cartesian coordinate system, the \( y \) and \( z \)-components of the velocity of ...

In a particular Cartesian coordinate system, the \( y \) and \( z \)-components of the velocity of a point-like object are zero and the \( x \)-component varies as given by the following function: \[ v_{x}(t)=2+5 t-3 t^{2}, \] where \( t \) is in seconds and \( v_{\mathrm{x}} \) is in meters per second. Part (a) Find the instantaneous velocity, in meters per second, at \( t=1.3 \mathrm{~s} \). Part (b) Find the instantaneous velocity, in meters per second, at \( t=2.35 \mathrm{~s} \). Part (c) Find the instantaneous velocity, in meters per second, at \( t=3.15 \mathrm{~s} \). Part (d) Find the instantaneous acceleration, in meters per square second, at \( t=1.3 \mathrm{~s} \). Part (e) Find the instantaneous acceleration, in meters per square second, at \( t=2.35 \mathrm{~s} \). Part (f) Find the instantaneous acceleration, in meters per square second, at \( t=3.15 \mathrm{~s} \). Part (g) If the particle was at \( x=0 \) at \( t=0 \), find the position, in meters, of the particle at \( t=1.3 \mathrm{~s} \). Part (h) If the particle was at \( x=0 \) at \( t=0 \), find the position, in meters, of the particle at \( t=2.35 \mathrm{~s} \). Part (i) If the particle was at \( x=0 \) at \( t=0 \), find the position, in meters, of the particle at \( t=3.15 \mathrm{~s} \).