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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

An object moves along the x-axis, its position given by x(t) = 2t2. Which of the following cannot be obtained from a graph of x vs. t? (a) The velocity at any instant (b) the acceleration at any instant (c) the displacement during some time interval (d) the average velocity during some time interval (e) the speed of the particle at any instant.

To determine
The acceleration, velocity, displacement, average velocity, and speed of the object from the position versus time graph.

Explanation

The position versus time graph divides the instantaneous positions of the object. The change in position at certain intervals gives the displacement of the object. The area under the graph gives the velocity of the object.

The area under the graph in certain intervals gives the average velocity in that interval. The ratio of the position and time at any instant gives the speed of the object; the change in the position versus time gives the instantaneous velocity.

Acceleration is the change in velocity with time. The acceleration can be found from the velocity versus time graph.

Conclusion:

Acceleration is the rate of change of velocity. Acceleration is the area under the velocity versus time graph. Acceleration cannot be found directly from a position versus time graph. Thus, option (b) cannot be determined from the x versus t graph...

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