document.write( "Question 430896: A point moves in a straight line such that its acceleration a is given by a=2(4-t)^1/2, 0≤t≤4. If it starts at rest, find an expreesion fot the velocity v where a =dv/dt. \n" ); document.write( "

Algebra.Com's Answer #299175 by Gogonati(855) $\"\"$ $\"About$

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Solution:The acceleration is, $\"a=2%284-t%29%5E%281%2F2%29\"$ , where, 0≤t≤4\r
\n" ); document.write( "\n" ); document.write( "To find the velocity of the point, we integrate the acceleration:\r
\n" ); document.write( "\n" ); document.write( " $\"int%282%284-t%29%5E%281%2F2%29%2C+dt%2C+0%2C+%0D%0A%0D%0A4%29\"$ = Substitute u=4-t then, du=-dt and dt=-du.\r
\n" ); document.write( "\n" ); document.write( " $\"2%2A+int%28u%5E%281%2F2%29%2C+du%2C+0%2C+4%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"%28-4%2F3%29u%5E%283%2F2%29\"$ , at (0, 4) \r
\n" ); document.write( "\n" ); document.write( "Substitute and have: 0-(-4/3)(4)^(2/3)=32/3 m/s. \n" ); document.write( "

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