Answer:
<em>The power output of the engine is 1,000 Watt</em>
Explanation:
<u>Mechanical Power
</u>
Power is the amount of energy transferred or converted per unit of time. In the SI, the unit of power is the watt, equal to one joule per second.
The power can be calculated as:
Where W is the work and t is the time.
The engine does a work of W=60,000 J during t=60 s. Calculate the power:
P = 1,000 Watt
The power output of the engine is 1,000 Watt
The position at time t is
x(t) = 0.5t³ - 3t² + 3t + 2
When the velocity is zero, the derivative of x with respect to t is zero. That is,
x' = 1.5t² - 6t + 3 = 0
or
t² - 4t + 2 = 0
Solve with the quadratic formula.
t = (1/2) [ 4 +/- √(16 - 8)] = 3.4142 or 0.5858 s
When t =0.5858 s, the position is
x = 0.5(0.5858³) - 3(0.5858²) + 3(0.5858) + 2 = 2.828 m
When t=3.4142 s, the position is
x = 0.5(3.4142³) - 3(3.4142²) + 3(3.4142) + 2 = -2.828 m
Reject the negative answer.
Answer:
The velocity is zero when t = 0.586 s, and the distance is 2.83 m
When the acceleration is zero, the second derivative of x with respect to t is zero. That is,
3t - 6 = 0
t = 2
The distance traveled is
x = 0.5(2³) - 3(2²) + 3(2) + 2 = 0
Answer:
When the acceleration is zero, t = 2 s, and the distance traveled is zero.
Whenever an object is falling, its potential energy
is decreasing and its kinetic energy is increasing.
Olivia's potential energy is decreasing and her kinetic energy
is increasing as she moves toward the right side of the picture,
all the way from W, through X, to the bottom of the arc.