Answer:
ρ = M / V = 2 g / .5 cm^3 = 4 g/cm^3
(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.
2^4/2^7 = 16/128 = 0.125
(1/2)^3= 0.125
1/8= 0.125
a and f are equivalent
Solution: (i) Density (ii) thermal
Liquids at lower temperatures have greater density when compared to liquids at higher temperatures.This is because, at higher temperatures, molecules have greater kinetic energy and hence they are spaced farther apart, when compared to molecules at lower temperatures. Thus, the colder layers of liquids are heavier than the warmer layers, which causes then to move down due to gravity. For the same reason, the hotter layers move upwards through the liquid.
When a liquid is heated, the molecules closest to the heat source have greater energy, their density becomes less and they move upwards. The colder layers sink downwards. The layers of the liquid which were cold initially, get heated and they travel upwards. As the process repeats, convection currents are set up in the liquid.
These currents transfer the thermal energy derived from the source throughout the liquid. The process stops when the entire liquid is at the same temperature.
Thus, convection currents occur in liquids due to temperature and <u>density</u> differences. Convection currents transfer <u>thermal</u> energy throughout a fluid.
Potential energy is measured by mass * gravity * height. So, the larger the mass on a roller coaster, the more potential energy it has.
Also, the higher it is, the more potential energy it has.