A 120V Microwave uses 8A of current. It runs for 15 hours over the course of a month. If electrical energy costs $0.11/KWh, what
1 answer:
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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 =
Answer:
m1/6 ( c )
Explanation:
since all the balls starts having the same momentum after the two collisions we will apply the principal of conservation of energy
After first collision
m1v = m1v1 + m2v2 --- ( 1 )
After second collision
m2v2 = m2v2 + m3v3 ---- ( 2 )
combining equations 1 and 2
m1v = m1v1 + m2v2 + m3v3 ----- ( 3 )
All balls moving at the same momentum ( p ) = m1v1 = m2v2 = m3v3
note ; 3p = m1v ∴ m3 = ----- ( 4 )
applying conservation of energy
3v = v1 + v2 + v3 ------- ( 5 )
also 3m1v1 = m1v = v1 = v/3 =
v2 + v3 = 8/3 v ----- ( 6 )
next eliminate V3 for equation 6 by applying conservation of energy and momentum
m1 = 2m2 ------ ( 7 )
now using p1 = p2 = m1v1 = 1/2 m1v1 hence v2 = 2v1 where v1 = 1/3 v
hence ; v2 = 2/3 v ------- ( 8 )
solving with equation 6 and 8
v3 = 2v ------ ( 9 ) ∴ v/v3 = 1/2 ---- ( 10 )
solving with equation 9 and 10
m3 = m1/3 * 1/2 = m1/6