Question

Figure 2-44 gives the acceleration $a$ versus time $t$ for a particle moving along an $x$ axis. The $a$ -axis scale is set by $a_{s}=12.0 \mathrm{~m} / \mathrm{s}^{2} .$ At $t=-2.0 \mathrm{~s}$ the particle's velocity is $7.0$ $\mathrm{m} / \mathrm{s}$. What is its velocity at $t=$ $6.0 \mathrm{~s} ?$

Name: Problem 82, Chapter 2: Fundamentals of Physics
Uploaded: 2021-07-20T13:13:49-08:00
Duration: 3 min 6 s
Channel: Donald Albin
Description: Figure 2-44 gives the acceleration a versus time t for a particle moving along an x axis. The a -axis scale is set by as=12.0 m / s^2 . At t=-2.0 s the particle's velocity is 7.0 m / s. What is its velocity at t= 6.0 s ?

   Figure 2-44 gives the acceleration $a$ versus time $t$ for a particle moving along an $x$ axis. The $a$ -axis scale is set by $a_{s}=12.0 \mathrm{~m} / \mathrm{s}^{2} .$ At $t=-2.0 \mathrm{~s}$ the particle's velocity is $7.0$ $\mathrm{m} / \mathrm{s}$. What is its velocity at $t=$ $6.0 \mathrm{~s} ?$

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 2, Problem 82

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Solved by Expert Donald Albin

07/20/2021

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At $t=-2.0 \mathrm{~s}$, the particle's velocity is $7.0$ $\mathrm{m} / \mathrm{s}$. We need to find the velocity at $t=6.0 \mathrm{~s}$. Show more…

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Figure 2-44 gives the acceleration $a$ versus time $t$ for a particle moving along an $x$ axis. The $a$ -axis scale is set by $a_{s}=12.0 \mathrm{~m} / \mathrm{s}^{2} .$ At $t=-2.0 \mathrm{~s}$ the particle's velocity is $7.0$ $\mathrm{m} / \mathrm{s}$. What is its velocity at $t=$ $6.0 \mathrm{~s} ?$

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Key Concepts

Initial Conditions in Kinematics

Initial conditions, such as the starting velocity of a particle, provide the necessary baseline from which changes in velocity are calculated. When the change in velocity is determined from the graph, it is added to the initial velocity to find the final velocity.

Acceleration as the Derivative of Velocity

This concept states that acceleration is the rate of change of velocity with respect to time. By understanding that acceleration is the derivative of velocity, one can integrate the acceleration function over a time interval to determine the change in velocity.

Area Under the Acceleration-Time Graph

The area under the acceleration versus time graph represents the change in velocity over a given time period. Computing this area, while accounting for the sign and magnitude of the acceleration, is essential for determining how much the velocity has increased or decreased.

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