The velocity-time graph of a body moving in a straight line...

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $8 \mathrm{~s}$ are (a) $12 \mathrm{~m}, 20 \mathrm{~m}$ (b) $14 \mathrm{~m}, 12 \mathrm{~m}$ (c) $16 \mathrm{~m}, 20 \mathrm{~m}$ (d) $12 \mathrm{~m}, 16 \mathrm{~m}$

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $8 \mathrm{~s}$ are
(a) $12 \mathrm{~m}, 20 \mathrm{~m}$
(b) $14 \mathrm{~m}, 12 \mathrm{~m}$
(c) $16 \mathrm{~m}, 20 \mathrm{~m}$
(d) $12 \mathrm{~m}, 16 \mathrm{~m}$

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Key Concepts

velocity-time graph

A velocity-time graph displays how an object's velocity changes over time and is a key visual tool in analyzing motion. The slope of the graph indicates acceleration, and the areas under the curve represent displacement or distance, depending on whether the velocity values are taken as signed or absolute values.

displacement

Displacement is the net change in an object's position, taking into account both magnitude and direction. It is computed by finding the algebraic sum (or net signed area) under the velocity-time graph over the given interval, which accounts for portions of the motion in opposite directions.

distance traveled

Distance traveled refers to the total length of the path covered by an object, without considering direction. It is calculated by summing the absolute areas under the velocity-time curve, ensuring that all segments of motion contribute positively to the total distance irrespective of their direction.

area under the curve

In the context of motion analysis, the area under the curve on a velocity-time graph quantifies displacement or distance traveled. For displacement, the signed areas (positive or negative based on direction) are summed, while for distance, the areas are taken in absolute terms to reflect total path length.

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