Question

Velocity time graph of a particle in straight line motion is in shape of a sernicircle of radius $R$ as shown in figure. Its average acceleration from $t=0$ to $t=R$ is (a) $0 \mathrm{~m} / \mathrm{s}^{2}$ (b) $1 \mathrm{~m} / \mathrm{s}^{2}$ (c) $R \mathrm{~m} / \mathrm{s}^{2}$ (d) $2 R \mathrm{~m} / \mathrm{s}^{3}$

   Velocity time graph of a particle in straight line motion is in shape of a sernicircle of radius $R$ as shown in figure. Its average acceleration from $t=0$ to $t=R$ is
(a) $0 \mathrm{~m} / \mathrm{s}^{2}$
(b) $1 \mathrm{~m} / \mathrm{s}^{2}$
(c) $R \mathrm{~m} / \mathrm{s}^{2}$
(d) $2 R \mathrm{~m} / \mathrm{s}^{3}$

Practice Problem in Physics for the JEE Main and Advanced

Abhay Kumar 2015 Edition

Chapter 2, Problem 27

Instant Answer

Solved by Expert Mahendra Rathore

01/17/2022

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At time $t=0$, the velocity is $0$ m/s. Show more…

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Velocity time graph of a particle in straight line motion is in shape of a sernicircle of radius $R$ as shown in figure. Its average acceleration from $t=0$ to $t=R$ is (a) $0 \mathrm{~m} / \mathrm{s}^{2}$ (b) $1 \mathrm{~m} / \mathrm{s}^{2}$ (c) $R \mathrm{~m} / \mathrm{s}^{2}$ (d) $2 R \mathrm{~m} / \mathrm{s}^{3}$

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Key Concepts

Average Acceleration

Average acceleration is defined as the total change in velocity divided by the total elapsed time. It summarizes the overall rate at which the velocity changes, independent of any variations in instantaneous acceleration during the motion.

Velocity-Time Graph

A velocity-time graph represents how an object's velocity varies with time. The slope of the graph at any point corresponds to the instantaneous acceleration, while the area under the curve between two time points gives the displacement of the object over that interval.

Graphical Analysis of Motion

Graphical analysis involves interpreting the shape and features of motion graphs to extract kinematic information. When a velocity-time graph exhibits a specific geometric shape, such as a semicircle, it can help in understanding the overall behavior of the object's motion, including how changes in velocity occur over time.

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