Difference between revisions of "009B Sample Midterm 2, Problem 3"

Revision as of 20:19, 6 February 2017

A particle moves along a straight line with velocity given by:

v(t)=-32t+200

feet per second. Determine the total distance traveled by the particle

from time $t=0$ to time $t=10.$

Foundations:
1. How are the velocity function $v(t)$ and the position function $s(t)$ related?
They are related by the equation $v(t)=s'(t).$
2. If we calculate $\int _{a}^{b}v(t)~dt,$ what are we calculating?
We are calculating $s(b)-s(a).$ This is the displacement of the particle from $t=a$ to $t=b.$
3. If we calculate $\int _{a}^{b}\|v(t)\|~dt,$ what are we calculating?
We are calculating the total distance traveled by the particle from $t=a$ to $t=b.$

Solution:

Step 1:

Final Answer:

@@ Line 10: / Line 10: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;
+|-
+|'''1.''' How are the velocity function <math>v(t)</math> and the position function <math>s(t)</math> related?
 |-
 |
+::They are related by the equation <math>v(t)=s'(t).</math>
+|-
+|'''2.''' If we calculate <math>\int_a^b v(t)~dt,</math> what are we calculating?
 |-
 |
+::We are calculating <math>s(b)-s(a).</math> This is the displacement of the particle from <math>t=a</math> to <math>t=b.</math>
+|-
+|'''3.''' If we calculate <math>\int_a^b |v(t)|~dt,</math> what are we calculating?
 |-
 |
+::We are calculating the total distance traveled by the particle from <math>t=a</math> to <math>t=b.</math>
 |}