(Solved): The position of an object (in metres) is given by the function \( s(t)=t^{4}-10 t^{3}+35 t^{2}- \) ...

The position of an object (in metres) is given by the function \( s(t)=t^{4}-10 t^{3}+35 t^{2}- \) \( 50 \mathrm{t}+24 \) where \( t \) is in seconds. a. Determine the velocity and acceleration functions for the object b. Determine the position, velocity and acceleration of the object at \( t=3.5 \mathrm{~s} \). c. At \( t=3.5 \mathrm{~s} \) is the object to the left or right of the origin? Explain how you know. d. At \( t=3.5 \mathrm{~s} \) is the object travelling to the left or right? Explain how you know. e. At \( t=3.5 \mathrm{~s} \) is the object speeding up or slowing down? Explain how you know.