Question

(a) What is the difference between 'distance travelled' by a body and its 'displacement'? Explain with the help of diagram.
(b) An ant travels a distance of 8 cm from P to Q and then moves a distance of 6 cm at right angles to PQ. Find its resultant displacement.

Answer 1

(a)

Distance		Displacement
1.	Distance has only magnitude, with no specified direction.	1.	Displacement has magnitude as well as direction.
2.	It is a scalar quantity.	2.	It is a vector quantity.
3.	Two different distances can be added directly.	3.	We have to follow the vector addition method to add displacements.

One difference in diagrammatic form is as follows:

Here the curved line is the distance traveled and the straight line is the magnitude of the displacement.

(b) We have to find the resultant displacement from the given diagram:

We have:
PQ = 8 cm and QR = 6 cm
Resultant displacement:
$$\begin{gathered} PR=\sqrt{P{Q}^2+Q{R}^2} \\ =\sqrt{64+36} \\ =\sqrt{100} \\ =\boxed{10\mathrm{cm}} \end{gathered}$$
The direction of this displacement is from P to R. If θ is the angle made by PR with PQ then,'

This is the angle made by the resultant with PQ.