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 $6 \mathrm{sec}$ are respectively
(a) $8 m, 16 m$
(b) $16 m, 8 m$
(c) $16 m, 16 m$
(d) $8 m, 8 m$

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Key Concepts

Area Under the Curve

The area under a velocity-time graph represents the displacement of an object over a given time interval. To find the total distance traveled, one must consider the absolute values of areas, especially when portions of the graph represent motion in opposite directions.

Velocity-Time Graph Analysis

A velocity-time graph visually represents how an object's velocity changes over time. In the study of kinematics, it is used to analyze motion by showing whether an object is speeding up, slowing down, or changing direction, and the slope of the graph can indicate acceleration while the area under the curve is related to displacement.

Displacement vs Distance Traveled

Displacement is the net change in position of an object and takes into account the direction of motion, whereas distance traveled is the total length of the path taken, regardless of direction. This distinction is important in physics to understand actual movement compared to directional changes.

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