Possible webpage title: What Remains Constant in One-Dimensional Kinematics?

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SUMMARY

The discussion centers on the relationship between average velocity and total displacement in one-dimensional kinematics, specifically when analyzing the area under velocity vs. time curves. The consensus is that while the total displacement (option D) remains constant from time t=0 to t=tf, average velocity (option B) is only valid under the condition that the time intervals are the same. Therefore, the answer key indicating D as the sole correct answer is accurate, although some participants argue that B could also be correct under specific conditions.

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  • Understanding of one-dimensional kinematics
  • Familiarity with velocity vs. time graphs
  • Knowledge of average velocity and total displacement concepts
  • Basic calculus, specifically derivatives and integrals
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Students and educators in physics, particularly those focusing on kinematics, as well as anyone interested in understanding the nuances of motion analysis and graph interpretation.

yti1211
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The area under both curves (velocity vs time) from t =0 to t =tf is the same. Which of the following quantities is the same from t =0 to t = tf?

A. average position B. average velocity C.average accerleration D. total displacement
E. jerk( the derivative of accerleration.

THE correct answer is D, but I think B and D both work, because average v = total displacement/time. so is the answer key wrong?

THANKSSSSSS
 
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Welcome to PF!

yti1211 said:
The area under both curves (velocity vs time) from t =0 to t =tf is the same. Which of the following quantities is the same from t =0 to t = tf?

A. average position B. average velocity C.average accerleration D. total displacement
E. jerk( the derivative of accerleration.

THE correct answer is D, but I think B and D both work, because average v = total displacement/time. so is the answer key wrong?

THANKSSSSSS

Hi yti1211! Welcome to PF! :smile:

hmm … I was going to say rubbish, you don't understand this …

but I think you're right! :biggrin:

(Unless, of course, the curves have different tfs:

D is correct even for different tfs, but B is correct only for the same tfs.)
 
haha, thanks tiny-tim! :))
 

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