The velocity-time graph of a body in one dimensional motion...

The velocity-time graph of a body in one dimensional motion is as shown. The distance covered by the body in 10 second is
(a) $25 \mathrm{~m}$
(b) $50 \mathrm{~m}$
(c) $100 \mathrm{~m}$
(d) $150 \mathrm{~m}$

Key Concepts

One-Dimensional Motion

One-dimensional motion involves movement along a straight line, where analysis can often be simplified by using graphs of velocity versus time. In such cases, understanding the relationship between velocity, time, and the area under the curve is essential for solving problems related to an object’s motion.

Displacement vs. Distance

Displacement is a vector quantity that measures the change in position of an object, while distance is a scalar quantity that represents the total length of the path traveled. In problems involving velocity-time graphs, especially when velocities do not change signs, the area under the curve directly corresponds to both the magnitude of displacement and the distance covered.

Area Under the Curve

The area under a velocity-time graph represents the displacement of the object during a specific time interval. This concept is fundamental in kinematics, as calculating the area (which may involve geometric shapes or integration) allows one to determine how far the object has moved.

Velocity-Time Graph

A velocity-time graph is a graphical representation of how an object's velocity changes over time. In kinematics, this graph is crucial because the area under the curve between two time points represents the displacement of the object, making it a powerful tool for analyzing motion in one dimension.

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