A particle moves from \(-4\,\mathrm{m}\) to \(9\,\mathrm{m}\). Find its displacement.

A cart moves from \(12\,\mathrm{m}\) to \(-3\,\mathrm{m}\). Find its displacement.

A particle returns to its starting position after moving around. What is its displacement?

An object starts at \(x_0=-2\,\mathrm{m}\) and has displacement \(7\,\mathrm{m}\). Find its final position.

An event starts at \(t_i=1.2\,\mathrm{s}\) and ends at \(t_f=5.8\,\mathrm{s}\). Find the elapsed time.

For \(x(t)=5-2t\), find \(x\) at \(t=3\,\mathrm{s}\) and interpret the sign.

A particle is at \(4\,\mathrm{m}\) at \(t=3\,\mathrm{s}\) and again at \(4\,\mathrm{m}\) at \(t=9\,\mathrm{s}\). What is its displacement over this interval?

A particle starts at \(1\,\mathrm{m}\), moves \(6\,\mathrm{m}\) in the positive direction, then \(2\,\mathrm{m}\) in the negative direction. Find final position, displacement, and distance traveled.

An object has three successive displacements: \(+3\,\mathrm{m}\), \(-9\,\mathrm{m}\), and \(+4\,\mathrm{m}\). Find the net displacement.

Particle A is at \(-2\,\mathrm{m}\). Particle B is at \(4\,\mathrm{m}\). Find their separation.

A coordinate origin is shifted so that the new coordinate is \(x'=x-5\,\mathrm{m}\). If \(x_i=2\,\mathrm{m}\) and \(x_f=11\,\mathrm{m}\), find the displacement in the new coordinate system.

The positive axis points west. A car moves from \(x=-20\,\mathrm{m}\) to \(x=-5\,\mathrm{m}\). State its displacement and direction.

A particle has \(x=0\). Does that mean it has zero displacement?

Show algebraically why shifting the origin by a constant \(c\) does not change displacement.

For \(x(t)=2t-3\), find the position at \(t=4\,\mathrm{s}\).

For \(x(t)=t^2-6\), find the displacement from \(t=1\,\mathrm{s}\) to \(t=4\,\mathrm{s}\).

Two labs report positions for the same particle, but they use different origins. Can their position values be compared directly?

Event A occurs at \(t=2.0\,\mathrm{s}\), and event B occurs at \(t=7.5\,\mathrm{s}\). Find the time interval from A to B.

A particle starts at \(-8\,\mathrm{m}\) and has displacement \(-6\,\mathrm{m}\). Find its final position.

A stopwatch reads \(0.25\,\mathrm{s}\) at the first mark and \(1.75\,\mathrm{s}\) at the second mark. Find the elapsed time.

A particle moves on a line with \(x_A=-3\,\mathrm{m}\) at \(t_A=1\,\mathrm{s}\), \(x_B=8\,\mathrm{m}\) at \(t_B=5\,\mathrm{s}\), and \(x_C=2\,\mathrm{m}\) at \(t_C=7\,\mathrm{s}\). Find the displacement and distance traveled from A to C.

Two coordinate systems are related by \(x'=2x-6\,\mathrm{m}\). A particle moves from \(x_i=4\,\mathrm{m}\) to \(x_f=-1\,\mathrm{m}\). Find \(\Delta x\) and \(\Delta x'\), then compare them.