You are on planet Dither, whose inhabitants often change their minds on how to choose a reference axis. At time \(t=0\), while standing \(2.0 \mathrm{~m}\) to the left of the origin of a reference axis for which the positive \(x\) direction points to the left, you launch a toy car that moves with increasing speed to the right. The car's \(x\) coordinate ( \(x\) component of the position) is given by \(x(t)=p+q t+r t^{2}\), where \(p=+2.0 \mathrm{~m}, q=-3.0 \mathrm{~m} / \mathrm{s}\), and \(r=-4.0 \mathrm{~m} / \mathrm{s}^{2}\).

(a) What is the equation of the car's \(x\) coordinate if the reference axis is flipped so that the positive direction points to the right? \((b)\) What is the equation of the car's \(x\) coordinate if the axis is kept in its original orientation (leftward is the positive direction) but the origin is moved to where you are standing?

(c) Draw a position-versus-time graph for each of the three combinations of axis direction and origin location.

(d) What is the \(x\) component of the car's displacement at \(t=4.0 \mathrm{~s}\) in each of these three axis/origin combinations?

(e) What is the \(x\) component of the car's velocity at this instant in each combination? ( \(f\) ) Explain why there is no physical difference in the answers to parts \(d\) and \(e\) even though some of the mathematical expressions you get look different from one another.