All are true except the first two.
(2.00 hours) x (3,600 seconds/hour) = 7,200 seconds
(9.00 minutes) x (60 seconds/minute) = 540 seconds
The record time = (7,200 + 540 + 21) = 7,761 seconds
Distance = (speed) x (time)
= (5.436 m/s) x (7,761 sec) =<span> 42,188.8 meters
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The official length of the marathon run is 42,195 meters.
If we divide that by the record time in the question, we get
5.4368... m/s .
Rounded to the nearest thousandth, that's 5.437 m/s.
If the question had given the speed as 5.437 instead of 5.436 ,
then we would have calculated the distance to be
(5.437 m/s) x (7,761 sec) =<span> 42,196.6 meters,
4.6 meters closer to the official distance than the answer we did get.
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For the answer to the question above, this is the maximum displacement, the spring has only elastic potential energy.
spring is constant @ 5 N/m
maximum displacement = 2 cm = 0.02 m
elastic potential energy = 1/2 kx²
= 0.5 x 5 x 0.02²
So the answer would be
= 0.001 Joules
The equation that describes the graph is y = 16.7x + 150.
<h3>What is the equation?</h3>
We have been given the graph of a certain function data set in physics. We know that the graph is the representation of data on cartesian coordinates. In this case, we are asked to find the equation of the graph in the form; y=mx+b
m = slope of the graph
b = intercept of the graph.
To obtain the slope;
m = y2 - y1/ x2 - x1
m = 400 - 200/ 16 - 4
m = 200/ 12
m = 16.7
Then we can see from the graph that the y - intercept is 150. Having these data, the equation that could describe the graph is now;
y = 16.7x + 150
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The amount of energy lost to air friction, given the data is 37.71 J
<h3>How to obtain the initial energy</h3>
- Initial velocity (u) = 15.1 m/s
- Mass (m) = 450 g = 450 / 1000 = 0.45 Kg
- Initial Energy (E₁) = ?
E₁ = ½mu²
E₁ = ½ × 0.45 × 15.1²
E₁ = 51.3 J
<h3>How to obtain the final energy</h3>
- Final velocity (u) = 19.89 m/s
- Mass (m) = 450 g = 450 / 1000 = 0.45 Kg
- Final Energy (E₂) = ?
E₂ = ½mv²
E₂ = ½ × 0.45 × 19.89²
E₂ = 89.01 J
<h3>How to determine the energy lost</h3>
- Initial Energy (E₁) = 51.3 J
- Final Energy (E₂) = 89.01 J
- Energy lost =?
Energy lost = E₂ - E₁
Energy lost = 89.01 - 51.3
Energy lost = 37.71 J
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