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 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

.

.