When a 4-kg ball is thrown upwards at 40 m/s, at what
1 answer:
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Answer:
B. x - t graph
Explanation:
A position-time (x-t) graph is a graph of the position of an object against (versus) time.
Generally, the slope of the line of a position-time (x-t) graph is typically used to determine or calculate the velocity of an object.
An instantaneous velocity can be defined as the rate of change in position of an object in motion for a short-specified interval of time. Thus, an instantaneous velocity is a quantity that can be found by measuring the slope of a line that is tangent to a point on the graph.
Hence, the x - t graph also referred to as the position-time graph is used for determining the instantaneous velocity from the slope.
<u>For example;</u>
Given that the equation of motion is S(t) = 4t² + 2t + 10. Find the instantaneous velocity at t = 5 seconds.
Solution.
Differentiating the equation, we have;
Substituting the value of "t" into the equation, we have;
S(5) = 42 m/s.
Answer:
P = 251,916.667 W
Cost = 2,267.25 cents
Explanation:
To solve this question we will use the Work Energy Theorem, which is
Where
= Change in Potential Energy
= Change in Kinetic Energy
Change in Potential Energy
Where
= Initial Potential Energy
= Final Potential Energy
= Mass of System = 10,000 kg
= Acceleration due to gravity = 9.81 m/s
= Initial Height = 0
= Final Height = 30 m
Inputting the values we get the answer for
Change in Kinetic Energy
Where
= Initial Kinetic Energy
= Final Kinetic Energy
= Mass of System = 10,000 kg
= Acceleration due to gravity = 9.81 m/s
= Initial Velocity = 0 m/2
= Final Velocity = 4 m/s
Inputting the values we get the answer for
Total Work
Inputting the values
a) Finding the useful Power Output
Where
= Power Output
= Work Done = 3,023,000J
= Time = 12s
Inputting the values
P = 251,916.667 W
b) Finding the Total Cost
Cost = $0.0900 x P/1000
Cost = $0.0900 x (251,916.667/1000)
Cost = $22.67 or 2,267.25 cents