That will depend on the units of the 3.0. We need to know if it's 3 feet, 3 yards, 3 meters, or 3 miles. Each one will have a different answer.
Kinetic energy: the energy of motion
Work: the change in kinetic energy
Power: the rate of work done
Explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion. Mathematically, it is given by:
![K=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
where
m is the mass of the object
v is its speed
The work done an object is the amount of energy transferred; according to the energy-work theorem, it is equal to the change in kinetic energy of an object:
![W=K_f - K_i](https://tex.z-dn.net/?f=W%3DK_f%20-%20K_i)
where
is the final kinetic energy
is the initial kinetic energy
Finally, the power is the rate of work done per unit time. Mathematically, ti can be expressed as
![P=\frac{W}{t}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BW%7D%7Bt%7D)
where
W is the work done
t is the time elapsed
Learn more about kinetic energy, work and power:
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The period of the pendulum is 8.2 s
Explanation:
The period of a simple pendulum is given by the equation:
![T=2\pi \sqrt{\frac{L}{g}}](https://tex.z-dn.net/?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7Bg%7D%7D)
where
L is the length of the pendulum
g is the acceleration of gravity
T is the period
We notice that the period of a pendulum does not depend at all on its mass, but only on its length.
For the pendulum in this problem, we have
L = 16.8 m
and
(acceleration of gravity)
Therefore the period of this pendulum is
![T=2\pi \sqrt{\frac{16.8}{9.8}}=8.2 s](https://tex.z-dn.net/?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7B16.8%7D%7B9.8%7D%7D%3D8.2%20s)
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Answer:
Kinetic energy = (1/2) (mass) (speed²)
Original KE = (1/2) (1430 kg) (7.5 m/s)² = 40,218.75 joules
Final KE = (1/2) (1430 kg) (11.0 m/s)² = 86,515 joules
Work done during the acceleration = (40218.75 - 86515) = 46,296.25 joules
Power = work/time = 46,296.25 joules / 9.3 sec = 4,978.1 watts .
Explanation:
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