(05.03 MC)

(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when $t=0$ and $t=3$ , and because the velocity function is continuous, you need only check the sign of $v(t)$ for values on the intervals (0, 3) and (3, 6).

We have, for instance $v(1)\approx-0.91$ and $v(4)\approx0.91>0$ , which means the particle is moving the positive direction for $3$ , or the interval (3, 6).

(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

$\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt$

which follows from the definition of absolute value. In particular, if $x$ is negative, then $|x|=-x$ .

The total distance traveled is then 4 ft.

(g) Acceleration is the rate of change of velocity, so $a(t)$ is the derivative of $v(t)$ :

$a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)$

Compute the acceleration at $t=4$ seconds:

$a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}$

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)

6 0

3 years ago

A town in east Texas recieved 10 inches of rain in two weeks. If it kept raining at this rate for a 31-day month, how much rain

Gelneren [198K]

The best way to approach this problem is to find out how much fell in week. As you know what two weeks is, you simply have to halve this, giving you that one week is 5 inches of rain. One you have this, you can multiply this by 4 (as this will give you 4 weeks, or 28 days), and this gives you 20 inches in 28 days. You should then find the odd three days. If you divide 5 by 7, this will give you the rain fall in one day. 5/7= 0.8 inches per day. You then have top multiply this by 3 (as you've got three odd days), and this gives you 2.4. You then have to add together 2.4 and 20, giving you 22.4
Therefore, if the rain continued to fall at the same rate for 31 days, it would receive 22.4 inches of rain.
Hope this helps :)

8 0

3 years ago