My Math Forum Speed-time graph

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 July 4th, 2012, 08:45 AM #1 Newbie   Joined: Apr 2012 Posts: 6 Thanks: 0 Speed-time graph This graph is a speed-time graph for a car accelerating from rest: http://imageshack.us/photo/my-images/82 ... dff54.png/ How long does it take the car to travel half the distance? I'm stuck on this question. How do I work this out? Thank you
 July 4th, 2012, 09:30 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Speed-time graph The distance d that the car travels is the area of the triangle under the velocity line: $d=\frac{1}{2}(t)(v)$ The acceleration a is the change in velocity with respect to time: $a=\frac{v-0}{t}\:\therefore\:v=at$ hence: $d=\frac{1}{2}at^2$ and so: $t=\sqrt{\frac{2d}{a}}$ If we let $t_1$ be the time to travel half the distance, and $t_2$ be the time to travel the entire distance, then we find: $\frac{t_1}{t_2}=\frac{\sqrt{\frac{d}{a}}}{\sqrt{\f rac{2d}{a}}}=\frac{1}{\sqrt{2}}$ hence: $t_1=\frac{1}{\sqrt{2}}t_2$

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