document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=942123>Question 942123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. Automotive engineers refer to the time rate of change of acceleration as the “ jerk.” Assume an object moves in one dimension such that its jerk J is constant.\r<BR>\n" );
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document.write( "(a) Determine expressions for its acceleration a(t), velocity v(t), and position x(t), given that its initial acceleration, velocity, and position are a0, v0, and x0, respectively.\r<BR>\n" );
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document.write( "(b) Show that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a2+=+a02+%2B+2+J+%28v+-+v0%29+ ALIGN=MIDDLE  ALT=\"+a2+=+a02+%2B+2+J+%28v+-+v0%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOTE: Finding the equations for motion with constant jerk is very similar to finding the equations for constant acceleration. Jerk is the derivative of acceleration ( J = da/dt ), and you already know that v = dx/dt and a = dv/dt. Just integrate in part (a) and rearrange in part (b) like we did in class when we derived the expressions for constant acceleration. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #574271 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=574271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large a(t) = a_0 + \int_{0}^{t} J \, dt' = a_0 + Jt\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large v(t) = v_0 + \int_{0}^{t} a(t) \, dt' = v_0 + a_0t + \frac{1}{2}Jt^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large x(t) = x_0 + \int_0^{t} v(t) \, dt' = x_0 + v_0t + \frac{1}{2}a_0t^2 + \frac{1}{6}Jt^3\">\r<BR>\n" );
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document.write( "b) You should specify what a_2 is. Not clear to us. </SPAN>\n" );
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