What is the Total Distance Traveled with Zero Acceleration?

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Homework Help Overview

The problem involves determining the total distance traveled by a particle defined by a cubic function of time, specifically when the acceleration is zero. The context is within the study of motion in physics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conditions under which acceleration is zero and how that relates to the total distance traveled. There are attempts to clarify the meaning of "sum" in the context of distance and to identify when the particle changes direction.

Discussion Status

The discussion is active, with participants exploring the relationship between acceleration, velocity, and distance. Hints have been provided regarding the times at which the acceleration and velocity are zero, and participants are engaging with these concepts to further their understanding.

Contextual Notes

There is some uncertainty regarding the interpretation of distance calculation and the specific time intervals involved. Participants are working within the constraints of the problem as posed, without additional information on the overall motion beyond the given function.

teng125
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the motion of a particle is defined by x=2(t^3) - 18(t^2) + 48t - 16 where x=meter and t=sec.determine the total distance traveled when the acceleration is zero.

the answer is 44m.

pls help...thanx...
 
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Hint:
At what instant (t-value) is the acceleration 0?
 
the value t=3 when the acc is zero
 
And how may you use that info to answer the original question?
 
oh,i found out d.it is the sum of t=0 to 3 rite??
 
What do you mean by "sum"?
 
the summation
 
Another hint: At what time does the particle change direction?
 
sorry,i not sure...
 
  • #10
At the moment the particle changes direction, what is its speed?
 
  • #11
the velocity is zero
 
  • #12
Thus, within the interval t=0 to t=3, is there any instant at which the velocity is zero?
 
  • #13
Right. So find when the particle's velocity is zero.
 
  • #14
the particle's velocity = zero when t=4s and 2s
 
  • #15
Right. So to find the distance traveled by the particle from t = 0 to t = 3 seconds find the distance traveled from t = 0 to t = 2 and from t = 2 to t = 3 and add them.
 
  • #16
ya,i found it...thanx...
 

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