Question

Find the distance traveled by the particle during the given time interval. Please help?? :(

Answer 1

The velocity function in meters per second for a particle moving along a line is given by

Answer 2

\[ v(t)=3t^2 -2t +1\]

Answer 3

0<t<3

Answer 4

Find the distance traveled by the particle during the given time interval.

(it should be 0 is less than equal to t is less than equal to 3)

Answer 5

Please help!

Answer 6

You have to integrate the equation with the limits of 0 to 3

Answer 7

Okay, I thought you integrate it if you want to find the displacement of the particle. But this is asking for distance traveled-isn't that asking for something different? :o

Answer 8

Since its only in one direction the displacement is the distance traveled

Answer 9

Ah, okay thanks, I'll try integrating it now

Answer 10

Let me know if it works for you

Answer 11

So I got 21 m/s.. ? I'll show my work:

Answer 12

\[\int\limits 3t^2 -2t +1\]
=\[3t^3/3 - 2t + 1\]
Then I use fundamental theorem of calculus part II :

=\[t^3-t^2+t\]
=\[(3^3-3^2+3) - (0^3-0^2+0)\]
=(21) - (0)
=21 m/s

Answer 13

okay, that's how I got 21. Is that correct?

Answer 14

Oops, sorry, I showed the second step wrong. But I integrated 2t and 1 to t^2 and t

Answer 15

Looks right

Answer 16

Thats what I got

Answer 17

Yay. Thanks so much!!

Answer 18

You bet!