# Kinematics of particles

1. Jan 1, 2006

### 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.

pls help.....thanx......

2. Jan 1, 2006

### arildno

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

3. Jan 1, 2006

### teng125

the value t=3 when the acc is zero

4. Jan 1, 2006

### arildno

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

5. Jan 1, 2006

### teng125

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

6. Jan 1, 2006

### arildno

What do you mean by "sum"?

7. Jan 1, 2006

### teng125

the summation

8. Jan 1, 2006

### Staff: Mentor

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

9. Jan 1, 2006

### teng125

sorry,i not sure.....

10. Jan 1, 2006

### Staff: Mentor

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

11. Jan 1, 2006

### teng125

the velocity is zero

12. Jan 1, 2006

### arildno

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

13. Jan 1, 2006

### Staff: Mentor

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

14. Jan 1, 2006

### teng125

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

15. Jan 1, 2006

### Staff: Mentor

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. Jan 1, 2006

### teng125

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