The position of a cart on a low-friction track can be represented by the equation \(x(t)=b+c t+e t^{2}\), where \(b=4.00 \mathrm{~m}, c=6.00 \mathrm{~m} / \mathrm{s}\), and \(e=0.200 \mathrm{~m} / \mathrm{s}^{2}\).

(a) Is the cart accelerating? If so, is the acceleration constant?

(b) What is the average velocity between \(t_{\mathrm{i}}=0.200 \mathrm{~s}\) and \(t_{\mathrm{f}}=0.400 \mathrm{~s}\) ?

(c) What is the velocity at \(t=0.200 \mathrm{~s}\) and at \(t=0.400 \mathrm{~s}\) ? \((d)\) What is the average acceleration between \(t_{\mathrm{i}}=0.200 \mathrm{~s}\) and \(t_{\mathrm{f}}=0.400 \mathrm{~s}\) ?

(e) What is the acceleration at \(t=0.200 \mathrm{~s}\) and at \(t=0.400 \mathrm{~s}\) ?