Unit 5: Motion and Forces
Position and Displacement
To locate an object means to ﬁnd its position relative to some reference point, often
the origin
(or zero point) of an axis such as the x axis in the figure. The positive
direction of the axis is in the direction of increasing numbers (coordinates), which
is to the right in the figure. The opposite is the negative direction.
A plus sign for a coordinate need not be shown, but a minus
sign must always be shown. Changing from position *x*_{1} to position *x*_{2} is called a displacement Δ*x*, where Δx = *x*_{2} - *x*_{1}_{.}
Note: Δ is a symbol used for representing change in quantity. Displacements to the right are always positive and to the left negative.
Example: A particle moves from *x*_{1}= 5m to position *x*_{2} = 15m gives Δx = *15m*_{} - *5m*_{}_{.}= 10m (a positive displacement); however a particle moving from *x*_{1}= 15m to position *x*_{2} = 5m = *5m*_{} - *15m*_{}_{.}= -10m (a negatve displacement)
The actual distance of the trip is irrelevant - it is only the original and final position that count.
Ignoring the sign of the displacement changes it from the vector (displacement) to a scalar (distance); while the magnitudes are the same the direction is very important and distinguishes vector from scalar quantities.
Questions:
Calculate the displacements in the following displacements:
(a) - 4m to 26m (b) 64m to 23m (c) -6m to 10m (d) -4m to -20m (e) -10m to -5m. |