'The acceleration time eraph of a particle moving in a...

'The acceleration time eraph of a particle moving in a straight line is as shown in figure. 'The velocity of the particle at time $t=0$ is $2 \mathrm{~m} / \mathrm{s}$. The velocity after 2 seconds will be: (a) $6 \mathrm{~m} / \mathrm{s}$ (b) $4 \mathrm{~m} / \mathrm{s}$ (c) $2 \mathrm{~m} / \mathrm{s}$ (d) $8 \mathrm{~m} / \mathrm{s}$

'The acceleration time eraph of a particle moving in a straight line is as shown in figure. 'The velocity of the particle at time $t=0$ is $2 \mathrm{~m} / \mathrm{s}$. The velocity after 2 seconds will be:
(a) $6 \mathrm{~m} / \mathrm{s}$
(b) $4 \mathrm{~m} / \mathrm{s}$
(c) $2 \mathrm{~m} / \mathrm{s}$
(d) $8 \mathrm{~m} / \mathrm{s}$

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Key Concepts

Acceleration-Time Graph

An acceleration-time graph displays how the acceleration of an object changes with respect to time. It is a visual tool used to understand an object's dynamics and can be analyzed to determine the change in velocity by computing the area under the curve during a specific time interval.

Integration of Acceleration

The process of integrating the acceleration function with respect to time is used to obtain the change in velocity. The area under the acceleration-time graph over a given time period represents the total change in velocity during that interval.

Initial Conditions

Initial conditions, such as the starting velocity of an object, are crucial for solving problems in kinematics. The initial velocity serves as a baseline value that must be adjusted by the integrated acceleration (or net change in velocity) to determine the final velocity.

Area Under the Curve

The area under the curve in an acceleration-time graph corresponds to the net change in velocity. Calculating this area allows one to add the resulting change to the initial velocity to find the final velocity at the end of the time period.

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