2000010802

Consider non-uniform motion of an object whose position as a function of time is given by \[ s=t^3-t^2+\frac12 t, \] where time \(t\) is measured in seconds and position \(s\) is measured in meters. Find the instantaneous acceleration of the object at time \(t = 2\) s. (Hint: Instantaneous acceleration can be expressed as the derivative of the velocity function with respect to time and since velocity is the derivative of position function, instantaneous acceleration is its second derivative: \(a(t)=\frac{\mathrm{d}v}{\mathrm{d}t}=\frac{\mathrm{d}^2s}{\mathrm{d}t^2}\).)