Question

An object moves in a straight line so that its velocity after t seconds is v(t). Determine the displacement and distance traveled by the object on the given time interval.
v(t) = 7 − 14 sin(πt) on [0,2]
I found the displacement to be 14.
But the distance stinks because of the intervals

Answer 1

why does the distance stink?

Answer 2

oh i see, goes backwards then forwards then backwards

Answer 3

\[14\sin(\pi t)=7\]
\[\sin(\pi t)=\frac{1}{2}\]
\[\pi t=\frac{\pi}{6}\]
\[t=\frac{1}{6}\] for the first one

Answer 4

ok my first comment was wrong
derivative is positive, then negative, then positive
so it goes forward then backward, then forward

forward on interval \((0,\frac{1}{6})\)

Answer 5

you good from there? next solve
\(\sin(\pi t)=\frac{1}{2}\)
\[\pi t=\frac{5\pi}{6}\]
\[t=\frac{5}{6}\] and break up your intervals accordingly

Answer 6

so don't include 1/6?

Answer 7

the interval is from0->2

Answer 8

integrate from 0 to 1/6
then from 1/6 tp 5/6
then from 5/6 to 2

Answer 9

it is negative on \((\frac{1}{6},\frac{5}{6})\) so integrate the negative of the function

Answer 10

I see. I did that but I guess I need the fraction for rather than the decimal form XP

Answer 11

you are looking for positive distnace

Answer 12

right, I got you
thanks :)