document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166452>Question 1166452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorboat accelerates uniformly from a velocity of 6.7 m/s to the west to a velocity of 1.4 m/s to the west. If its acceleration was 3.4 m/s^2 to the east,<BR>\n" );
document.write( "how far did it travel during the acceleration? Answer in units of m. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852753 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2138)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a problem in one-dimensional kinematics that can be solved using the time-independent equation relating velocity, acceleration, and displacement.\r<BR>\n" );
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document.write( "## 📐 Kinematics Calculation\r<BR>\n" );
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document.write( "1.  **Define Direction and Variables:**<BR>\n" );
document.write( "    Let **West be the positive direction** ($+$).\r<BR>\n" );
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document.write( "    * Initial Velocity ($\vec{v}_i$): $6.7 \text{ m/s}$ West $\implies v_i = +6.7 \text{ m/s}$<BR>\n" );
document.write( "    * Final Velocity ($\vec{v}_f$): $1.4 \text{ m/s}$ West $\implies v_f = +1.4 \text{ m/s}$<BR>\n" );
document.write( "    * Acceleration ($\vec{a}$): $3.4 \text{ m/s}^2$ East $\implies a = -3.4 \text{ m/s}^2$\r<BR>\n" );
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document.write( "2.  **Select the Kinematic Equation:**<BR>\n" );
document.write( "    Since the time is not given, we use the equation that relates the final velocity, initial velocity, acceleration, and displacement ($\Delta x$):<BR>\n" );
document.write( "    $$v_f^2 = v_i^2 + 2a \Delta x$$\r<BR>\n" );
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document.write( "3.  **Solve for Displacement ($\Delta x$):**<BR>\n" );
document.write( "    $$\Delta x = \frac{v_f^2 - v_i^2}{2a}$$\r<BR>\n" );
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document.write( "4.  **Substitute Values and Compute:**<BR>\n" );
document.write( "    $$\Delta x = \frac{(1.4 \text{ m/s})^2 - (6.7 \text{ m/s})^2}{2(-3.4 \text{ m/s}^2)}$$<BR>\n" );
document.write( "    $$\Delta x = \frac{1.96 \text{ m}^2/\text{s}^2 - 44.89 \text{ m}^2/\text{s}^2}{-6.8 \text{ m/s}^2}$$<BR>\n" );
document.write( "    $$\Delta x = \frac{-42.93 \text{ m}^2/\text{s}^2}{-6.8 \text{ m/s}^2}$$<BR>\n" );
document.write( "    $$\Delta x \approx 6.3132 \text{ m}$$\r<BR>\n" );
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document.write( "The distance traveled is the magnitude of the displacement.\r<BR>\n" );
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document.write( "The distance the motorboat traveled during the acceleration is **$6.31$ m**. </SPAN>\n" );
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