Answer:
When the rock is on top of the building, it does not move, so it only has potential energy.
The potential energy can be written as:
U = m*g*h
where m is the mass, g is the gravitational acceleration, h is the height.
Now, as the rock starts to fall down, the potential energy transforms into kinetic energy.
K = (m/2)*v^2
Where v is the velocity.
When the rock hits the ground, all the potential energy has ben converted into kinetic energy, then:
U = K
m*g*h = (m/2)*v^2
Here we can isolate v:
v = √(2*g*h)
and g = 9.8m/s^2
h = 10.5m
v = √(2*10.5m*9.8m/s^2) = 14.34m/s
Now the second question:
"what is the Plot the position, velocity and acceleration vs. time"
I suppose that you need to select the correct plot for each thing, the images are not given, so let's analyze how each plot is:
The motion equations are:
Acceleration:
Here we have only the gravitational acceleration, so we can write:
a(t) = -g
This is a constant, the graph will be a horizontal line at y = -g.
Velocity:
We integrate the acceleration over time, the constant of integration is the initial velocity, that in this case is zero.
v(t) = -g*t
This is a linear equation with slope equal to -g, and y-intercept equal to zero.
Position.
We integrate again over time, this time the constant of integration will be the initial height of the rock = 10.5m
The equation is:
p(t) = -(g/2)*t^2 + 10.5m
This is a quadratic equation with a negative leading coefficient, so the arms go downwards.
