What is the Total Distance Traveled with Zero Acceleration?

[teng125]

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...

 

[arildno]

Hint:
At what instant (t-value) is the acceleration 0?

 

[teng125]

the value t=3 when the acc is zero

 

[arildno]

And how may you use that info to answer the original question?

 

[teng125]

oh,i found out d.it is the sum of t=0 to 3 rite??

 

[arildno]

What do you mean by "sum"?

 

[teng125]

the summation

 

[Doc Al]

Another hint: At what time does the particle change direction?

 

[teng125]

sorry,i not sure...

 

[Doc Al]

At the moment the particle changes direction, what is its speed?

 

[teng125]

the velocity is zero

 

[arildno]

Thus, within the interval t=0 to t=3, is there any instant at which the velocity is zero?

 

[Doc Al]

Right. So find when the particle's velocity is zero.

 

[teng125]

the particle's velocity = zero when t=4s and 2s

 

[Doc Al]

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.

 

[teng125]

ya,i found it...thanx...