Question

Acceleration-time graph of a particle starting from rest and moving along a straight line is as shown. The velocity of the particle after $4 \mathrm{~s}$ is $(\mathrm{in} \mathrm{m} / \mathrm{s})$. (a) 10 (b) 20 (c) 15 (d) 30

Name: Problem 12, Chapter 2: IIT JEE Super Course in Physics: Mechanics I
Uploaded: 2021-06-07T17:45:26-08:00
Duration: 1 min 42 s
Channel: Satpal Satpal
Description: Acceleration-time graph of a particle starting from rest and moving along a straight line is as shown. The velocity of the particle after 4 s is (in m / s). (a) 10 (b) 20 (c) 15 (d) 30

   Acceleration-time graph of a particle starting from rest and moving along a straight line is as shown. The velocity of the particle after $4 \mathrm{~s}$ is $(\mathrm{in} \mathrm{m} / \mathrm{s})$.
(a) 10
(b) 20
(c) 15
(d) 30

IIT JEE Super Course in Physics: Mechanics I

Trishna Knowledge… 1st Edition

Chapter 2, Problem 12

Instant Answer

Solved by Expert Satpal Satpal

06/07/2021

Step 1

The area under the acceleration-time graph gives us the change in velocity. Show more…

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Acceleration-time graph of a particle starting from rest and moving along a straight line is as shown. The velocity of the particle after $4 \mathrm{~s}$ is $(\mathrm{in} \mathrm{m} / \mathrm{s})$. (a) 10 (b) 20 (c) 15 (d) 30

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Key Concepts

Initial Conditions

Initial conditions, such as a particle starting from rest, provide the necessary baseline or starting value for integration. They ensure that the calculation of velocity accurately reflects the subsequent change due only to the integration of acceleration over time.

Integration in Kinematics

Integration is a mathematical tool used to accumulate the effects of a rate of change. In kinematics, integrating acceleration with respect to time yields the velocity. This process links the instantaneous rate of change (acceleration) to the overall change in motion (velocity), making it essential for solving motion problems.

Acceleration-Time Graph

An acceleration-time graph is a visual representation of how acceleration varies with time. The key idea is that the area under this curve over a given time interval represents the change in velocity during that interval, which is critical when determining motion characteristics of a particle.

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