What would become of the earth's orbit (which you may consider to be a circle) if half of the sun's mass were suddenly to disappear? would the earth remain bound to the sun? [hints: consider what happens to the earth's ke and pe at the moment of the great disappearance. the virial theorem for the circular orbit (problem 4.41) with this one.] treat the sun (or what remains of it) as fixed.

Atrain departs from its station at a constant acceleration of 5 m/s. what is the speed of the train at the end of 20s?

You have been consulted by the mobile phone company hookup about a new augmented reality product called “brows”. they want to develop an alternative to google glasses, which, you recall, is a proposed new product which plans to superimpose a whole range of wireless google services over the user’s ordinary vision of the world. these appear in little circles and ovals, and let you phone people, take photographs, navigate across cities and inside buildings, find shops and update your social media. brows would do this too, but not be limited to special google services. the user would wear a small cylinder-shaped device designed to fit on top of their existing eyewear (glasses or sunglasses). it would project a reversed image onto the inside of the lenses, the reflection of which would be in focus for the user. instead of voice control, the user would control the device by eye and neck movements, which the device would track. the device would connect via bluetooth to the user’s phone, which would supply most of the computing power and wireless connectivity. hookup also wants to know what existing services would be most in demand, and which would not work well with brows. using your knowledge of augmented reality, wearable technology and interface design, is the project feasible? if not, why not? if feasible, how could the product need to be modified for a better experience?

Using the work energy theorem. what is the velocity of a 850kg car after starting at rest when 13,000j of work is done to it.