The number of protons determines the element. Many elements also have many isotopes. Such as carbon-14 Carbon-12 and carbon-10.
(a) This is a freefall problem in disguise - when the ball returns to its original position, it will be going at the same speed but in the opposite direction. So the ball's final velocity is the negative of its initial velocity.
Recall that

We have
, so that

(b) The speed of the ball at the start and at the end of the roll are the same 8 m/s, so the average speed is also 8 m/s.
(c) The ball's average velocity is 0. Average velocity is given by
, and we know that
.
(d) The position of the ball
at time
is given by

Take the starting position to be the origin,
. Then after 6 seconds,

so the ball is 42 m away from where it started.
We're not asked to say in which direction it's moving at this point, but just out of curiosity we can determine that too:

Since the velocity is positive, the ball is still moving up the incline.
Answer:
v0 = 25 m/s
vf = 0 m/s
a = -9.80 m/s^2
change in x = 31.89m
but that's only 1/3 of the hight, so i time it by 3 to get 96m
21/12 is equal to 1 3/4 hope this helps!
<span>The amount of heat energy needed to increase the temperature of a substance by </span>

<span> is given by:
</span>

<span>
where m is the mass of the substance, Cs is its specific heat capacity and </span>

<span> is the increase in temperature of the substance.
In this problem, we have a certain mass m of gold, with specific heat capacity </span>

<span>, to which we add Q=2825 J of energy. Its temperature increases by </span>

<span>. Therefore, if we re-arrange the previous equation, we can find the mass of the block of gold:
</span>

<span>
So, the correct answer is B.</span>