Consider a \(2.0-\mathrm{kg}\) object that moves along the \(x\) axis according to the expression \(x(t)=c t^{3}\), where \(c=+0.120 \mathrm{~m} / \mathrm{s}^{3}\).

(a) Determine the \(x\) component of the object's average velocity during the interval from \(t_{\mathrm{i}}=0.500 \mathrm{~s}\) to \(t_{\mathrm{f}}=1.50 \mathrm{~s}\).

(b) Repeat for the interval from \(t_{\mathrm{i}}=0.950 \mathrm{~s}\) to \(t_{\mathrm{f}}=1.05 \mathrm{~s}\).

(c) Show that your results approach the \(x\) component of the velocity at \(t=1.00 \mathrm{~s}\) if you continue to reduce the interval by factors of 10 . Use all significant digits provided by your calculator at each step.