Question

A particle moves along a line so that its velocity at time t is v(t)=t2-t-12. Find the distance traveled during this time period. (Please see the image!) Thank you!!

(b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so
O on the interval [2, 4] and v(t) > v
%3|
v(t) < v
O on [4, 6].
Thus, from this equation, the distance traveled is
4
9.
|v(t)| dt
[-v(t)] dt +
v(t) dt
4.
4
9.
= | (-?+t + 12)
| (? - t - 12) dt
dt +
16
,3
+ 12t
- 12t
2
+
2
14
82
3

Image Transcription

(b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so O on the interval [2, 4] and v(t) > v %3| v(t) < v O on [4, 6]. Thus, from this equation, the distance traveled is 4 9. |v(t)| dt [-v(t)] dt + v(t) dt 4. 4 9. = | (-?+t + 12) | (? - t - 12) dt dt + 16 ,3 + 12t - 12t 2 + 2 14 82 3

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Tagged in
Math
Calculus

Integration