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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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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

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