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# The acceleration of a particle moving back and forth on a ## Problem 78E Chapter 5.5

University Calculus: Early Transcendentals | 2nd Edition

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Problem 78E

The acceleration of a particle moving back and forth on a line is for all t. If s=0 and v=8 m/sec when t = 0, find s when t =1 sec.

Step-by-Step Solution:

Step 1 of 7</p>

Here, we have to find the position of the moving particle s when time .

Given that the acceleration for all t.

It is also given that and when .

Step 2 of 7</p>

We have .

We know that acceleration is the derivative of velocity.

Thus, we get the velocity as   . .

Step 3 of 7</p>

We have the condition that when .

Therefore, we get  .

Therefore, we get the velocity as .

Step 4 of 7</p>

Now, we can get the position s by simply integrating the velocity.

Therefore, we get  . .

Step 5 of 7

Step 6 of 7

##### ISBN: 9780321717399

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The acceleration of a particle moving back and forth on a

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Get Full Access to University Calculus: Early Transcendentals - 2 Edition - Chapter 5.5 - Problem 78e

Get Full Access to University Calculus: Early Transcendentals - 2 Edition - Chapter 5.5 - Problem 78e