7. For a constant force, suppose the duration of
impact on an object is doubled.
a. How much is the impulse increased?
b. How much is the resulting change in
momentum increased? (7.2)

a. impulse increases by the square of the force.

b. momentum also increases

Explanation:

As we know, force is defined as the product of mass and acceleration of the object. Impulse is nothing but the impulse of an object moving is defined as the integral of all the forces acting on the object. As we know that force is a vector quantity and hence the impulse. Since impulse is the integral of all the forces. Here, in the question, it is given that the force is doubled then if you integrate then you get a square function. So, the impulse increases by square function.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.