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# Suppose that when launching an 800-kg roller coaster car an electromagnetic propulsion system exerts a force of $5.7x^2 + 1.5x$ newtons on the car at a distance $x$ meters along the track. Use Exercise 31(a) to find the speed of the car when it has traveled 60 meters.

## 32.14 $\mathrm{m} / \mathrm{s}$

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Applications of Integration

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

So for this question, we're gonna ply the physical love beyond connect kinetic energy. So the work equals to Albert Connect Angeles equals to have a and B squared. And, uh, the work is actually the force. The eggs from the position, the starting position, the position which is steeples to 0 to 60 in our force function equals two, five and seven X squared waas 115 minutes. So the work gonna be done? But is this force gonna be gonna be fine on seven X cubed over three plus. And what about X squared over two from 2 0 to 60 which is equals two four points. 13131 times turned to buy has been large, Jule. And by this equation, we're gonna solve for being the speed equals two, two times the work over the mess and we give it a square root so hands we can tattoo it this speed by plugging in the work and the mess. And within the Indian of with four on 131 touch to the fight over 400 that equals two 32 points. 14 be those positions. It's all results

University of Illinois at Urbana-Champaign

#### Topics

Applications of Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp