A warehouse robot rolls along an aisle's number line from the x₀ = +2 m mark to the x = −5 m mark. How far does the robot end up from where it started, and which way?
You've already seen displacement as the change in position. On a number line, a change in position is a subtraction.
On a number line, displacement is written Δx. The Greek letter Δ, delta, means 'the change in'. So Δx reads 'the change in position', and that's exactly what a displacement is. Δ on its own just means 'change in'; the symbol for displacement is the pair together, Δx.
Both positions are in meters, so their difference, the displacement, comes out in meters. Keep every sign: the robot goes from x₀ = +2 m to x = −5 m, so its displacement is Δx = (−5) − (+2) = −7 m.
The sign of Δx is the direction of the change: negative means the object ended farther toward the negative side than it started.
A cart rolls from x₀ = −4 m to x = +6 m along a track's number line. What is the cart's displacement?
Write down the values in the question:
x₀ = −4 m
x = +6 m
Δx = ?
Write down the equation:
Δx = x − x₀
Substitute in the values:
Δx = (+6) − (−4)
Simplify:
Δx = +10 m
A skater glides from x₀ = +3 m to x = +11 m. Enter the displacement Δx in meters, including the sign.
A remote-controlled car drives from x₀ = +4 m to x = -8 m. Enter the displacement Δx in meters, including the sign.
A crab scuttles from x₀ = -6 m to x = -1 m. Enter the displacement Δx in meters, including the sign.
A luggage cart moves from x₀ = -2 m to x = -9 m along a terminal corridor. Enter the displacement Δx in meters, including the sign.
Measured from a depot, a maintenance car starts at x₀ = +120 m and stops at x = -80 m. Enter the car's displacement Δx in meters, including the sign.
A car moves from x₀ = -3 m to x = +9 m, measured from a platform mark. Enter the car's displacement Δx in meters, including the sign.