The whole point of this problem is to check how well you understand
the definitions of a few important quantities, like velocity, speed, distance,
displacement etc.
Before we begin, I just want to mention that 'MPG' is not a unit of either
velocity or speed, but I think I know what you mean.
-- For some reason, Ms. Eaddy rode 100 miles north on the train, then
stayed aboard while the train turned around and took her 150 miles south.
The total distance she rode was (100 + 150) = 250 miles. But she ended up
50 miles south of where she began.
-- Displacement for the whole trip = distance and direction from the start point
to the finish point.
Displacement = 50 miles south
-- Average velocity = (displacement) / (time)
50 miles south / 3.5 hours = <u>14.29 miles per hour south</u>
Beats.
When two sound waves of different frequency approach your ear, the alternating constructive and destructive interference causes the sound to be alternatively soft and loud - a phenomenon which is called "beating" or producing beats. The beat frequency is equal to the absolute value of the difference in frequency of the two waves.
Answer:
The work done is 205 kJ.
Explanation:
Hi there!
Work can be calculated using the following equation:
W = F · Δx
Where:
W = work
F = applied force
Δx = displacement
In this case, the force varies with the position, so we can divide the traveled distance in very small parts and calculate the work done over each part of the trajectory. Then, we have to sum all the works and we will obtain the work done from the initial position (xi) to the final position (xf). This is the same as saying:
W = ∫ F · dx
F = 3.6 N/m³ · x³ - 76 N
W = ∫ (3.6 x³ - 76)dx
W = 0.9 x⁴ - 76x
Evaluating from xi to xf:
W = 0.9 N/m³ (21.9 m)⁴ - 76 N · 21.9 m - 0.9 N/m³(5.41 m)⁴ + 76 N · 5.41 m
W = 205 kJ
Initial velocity = Vo= 25 m/s
Final velocity = V = x
Acceleration= a = 6 m/s^2
time= t = 4 seconds
Appy the equation:
V = Vo + at
Replacing:
V = 25 + 6(4) = 25 + 24 = 49 m/s
