Answer:
a) 
b) 
c) 
d) Displacement = 22 m
e) Average speed = 11 m/s
Explanation:
a)
Notice that the acceleration is the derivative of the velocity function, which in this case, being a straight line is constant everywhere, and which can be calculated as:
Therefore, acceleration is
b) the functional expression for this line of slope 4 that passes through a y-intercept at (0, 3) is given by:
c) Since we know the general formula for the velocity, now we can estimate it at any value for 't", for example for the requested t = 1 second:
d) The displacement between times t = 1 sec, and t = 3 seconds is given by the area under the velocity curve between these two time values. Since we have a simple trapezoid, we can calculate it directly using geometry and evaluating V(3) (we already know V(1)):
Displacement = 
e) Recall that the average of a function between two values is the integral (area under the curve) divided by the length of the interval:
Average velocity = 
Good morning.
We see that
The magnitude(norm, to be precise) can be calculated the following way:
Now the calculus is trivial:
Answer: at the same time
Explanation: in a vacuum, there isnt air, right? so there isnt gravity pushing down on the heavier object, so they will both land at the same time.
good? :)
To minimize the material usage we have to have the volume requested with the minimum surface area.
The volume is:
And the surface is:
From the first equation we get:
I will use k instead of a number just for the conveince.
We plug this into the second equation and we get:
To find the minimum of this function we have to find the zeros of its first derivative.
Sx will denote the first derivative with respect to x and Sy will denote the first derivative with respect to Sy.
Now let both derivatives go to zero and solve the system (this will give us the so-called critical points).
Now we plug in the first equation into the other and we get:
Now we can calculate y:
And finaly we calculate z:
And finaly let's check our result:
