What is path length? What is displacement?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Path length is the total distance covered by an object during its motion between two points. It is a scalar quantity,meaning it has magnitude but no direction.
Displacement is the change in the position of an object in a particular interval of time. It is defined as the difference between the final position $(x_2)$ and the initial position $(x_1)$: $\Delta x = x_2 - x_1$. Displacement is a vector quantity,as it has both magnitude and direction.
Example: Consider a car moving from origin $O$ $(x=0)$ to point $P$ $(x=360 \ m)$ and then back to point $Q$ $(x=240 \ m)$.
$1$. Path length: The total distance covered is $OP + PQ = 360 \ m + (360 \ m - 240 \ m) = 360 \ m + 120 \ m = 480 \ m$.
$2$. Displacement: The displacement is the final position minus the initial position: $\Delta x = x_Q - x_O = 240 \ m - 0 \ m = +240 \ m$. The positive sign indicates the direction is along the positive $x$-axis.

Explore More

Similar Questions

$A$ particle moves a distance of $5 \ m$ in the $+x$ direction. Find its displacement.

In which of the following examples of motion can the body be considered approximately a point object:
$(a)$ $A$ railway carriage moving without jerks between two stations.
$(b)$ $A$ monkey sitting on top of a man cycling smoothly on a circular track.
$(c)$ $A$ spinning cricket ball that turns sharply on hitting the ground.
$(d)$ $A$ tumbling beaker that has slipped off the edge of a table.

Distinguish between path length and displacement.

Which among path length and displacement cannot be zero for a moving object?

The position vector of a moving particle at time $t$ is $r = 3 \hat{i} + 4t \hat{j} - t \hat{k}$. Its displacement during the time interval $t = 1 \ s$ to $t = 3 \ s$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo