Mechanics | Relativity Answers

Find the speed at which the mass of a particle will be double?

Hi, I have been reading the brief history of time by Stephen Hawking and have been greatly enjoying it. In the second chapter he mentions the fact that time is slower when in proximity with a large mass such as the earth. So a twin on top of a mountain would age faster than his counterpart at sea level. He credits this phenomenon to the energy of light, saying that the energy of light decreases as gravity decreases. I was wondering how the energy of light can vary but its speed remain constant. Since high school I have been taught that if you change an objects energy you are also changing its gravitational potential or velocity. Any reply will be greatly appreciated.
Abhi.

when water fills a submarines floating tanks,overall density of submarine
a.decreases
b.staysa the same
c.increases
d.reduces the buoyant force

Slope of distance time graph of moving body is given as speed and slope of displacement-time graph of moving body is given as velocity. Justify ?

A 1030. kg automobile is pulled by a horizontal tow line with a net force of 834 N. What is the acceleration of the auto?

a ball is projected upwards from the top of a tower with a velocity of 50m/s making an angle of 30 degree with the horizontal. the hieght of the tower is 70m. after how many seconds from the instant of throwing will the ball reach the ground?

A boy wants to throw a letter wrapped over a stone to his friend across the street 40m wide the boy's window is 10m below friend's window .how should he throw it ?

What I'm going to ask is very confusing for me. In my Calculus book, I read;

s(t) = distance a particle travels from time '0' to 't'.
v(t) = velocity of a particle at time 't'.
a(t) = acceleration of a particle at time 't'.

My first question is; Are velocity, distance, and acceleration only the function of time?
If they are not, then in which case they are only the functions of time? Because, in the above three functions, they seem to be the function of time only.

what is range of gravitation and at which height gravity is zero

the diameter of an automobile wheel with its tire is 23 inches. how many revolutions does the wheel make in going a mile? and in going kilometer?