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At t=0, a particle is at rest at the origin. Its acceleration is 2 , m/s² for the first 3 seconds and -2 , m/s² for the next 3 seconds. Plot the acceleration versus time and velocity versus time graph. Also, find the displacement of the object during this time interval.

User Dmoebius
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Final answer:

To plot the acceleration versus time graph, split the time interval into two parts: 0-3 seconds and 3-6 seconds. The velocity versus time graph will have a positive slope for the first 3 seconds and a negative slope for the next 3 seconds. The displacement of the object during this time interval is 9 meters.

Step-by-step explanation:

To plot the acceleration versus time graph, we can split the given time interval into two parts: 0-3 seconds and 3-6 seconds. For the first 3 seconds, the acceleration is 2 m/s², and for the next 3 seconds, it is -2 m/s². So the acceleration versus time graph will have a positive slope of 2 for the first 3 seconds and a negative slope of -2 for the next 3 seconds.

To plot the velocity versus time graph, we can integrate the acceleration versus time graph. By integrating the positive slope segment (2 m/s²) from 0-3 seconds, we get a linear velocity versus time graph with a positive slope. By integrating the negative slope segment (-2 m/s²) from 3-6 seconds, we get a linear velocity versus time graph with a negative slope.

The displacement of the object can be calculated by integrating the velocity versus time graph. Since the object is at rest initially, the displacement during the first 3 seconds is 0. Then, during the next 3 seconds, the object has a constant velocity. So the displacement is given by the formula: displacement = initial velocity * time + 0.5 * acceleration * time^2. Substituting the values, we get displacement = 0 + 0.5 * 2 * 3^2 = 9 meters.

User Paulo Cheque
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