Basically, we want to see the distance in terms of thickness. So, for this rectilinear motion at constant acceleration, the equation to be used is:
x = v₀t + 0.5at²
First, let's determine t using the equation:
a = |v - v₀|/t
300 m/s² = |0 - 92.8 km/h * 1,000 m/1 km * 1 h/3600 s|/t
t = 0.086 seconds
x = (92.8 km/h * 1,000 m/1 km * 1 h/3600 s)(0.086 s) + 0.5(300 m/s²)(0.086 s)²
x = 3.33 meters
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:
The answers are:
<u>39:</u>
a - 1 mile
b - 0 miles
<u>40:</u>

<u>41:</u>

Why?
Solving 39:
To answer the questions, we need to remember that distance and displacement are different things. Distance refers to the total "ground" covered during motion, while displacement refers to how far is the object/body from its starting point.
So,
<u>39:</u>
a - the total distance traveled corresponds to the length of the track which is 1 mile.
b - The displacement is equal to 0 because they finished at the starting point, the distance between the starting and the finishing point is equal to 0.
<u>40:</u>
We can solve the problem using one of the given equations:

Since we know all the information, we just need to substitute it into the equation:

So, the car's acceleration was -4m/s2 (the car was reducing its speed)
<u>41:</u>
We can solve the problem using one of the given equations (Pythagorean Theorem):


The distance will be:

Have a nice day!
Answer: To "hole the ball: on the very first putt is requered is required a 7.08 m displacement at an angle 11.03° north of east.
Explanation:
Let's add each stroke as vectors
- Due east direction: 4.6 m + 2.5 cos(20°) m ≅ 6.95 m
- Due north direction: 0.5 m + 2.5 sin(20°) m ≅ 1.35 m
So the total displacement is

and the direction

I would say either A or B