(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

(b) The velocity after 3 seconds is

(c) The particle is at rest when its velocity is zero:

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,

By definition of absolute value, we have

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to

Answer:
of means to multiple so it would equal 4 so the answer is false
C. because her distance from home is decreasing
180 cm. it is that answer because ...
K H D U D C M
71 m times 100 is 180
The answer is 24. it works like this. you subtract 2 from 12 and get 10. then add 5 to 10 to get 15. then subtract 2 from 15 and get 13. 13+5 is 18. and so on