Power and energy Power and energy are often used interchangeably, but they are quite different. Energy is what makes mattermove or heat up. It is measured in units of joules or Calories,where 1 Cal = 4184 J. One hour of walking consumes roughly106J, or 240 Cal. On the other hand, power is the rate at whichenergy is used, which is measured in watts, where 1 W = 1 J/s.Other useful units of power are kilowatts 11 kW = 103W2 and megawatts 11 MW = 106 W2. If energy is used at a rateof 1 kW for one hour, the total amount of energy used is1 kilowatt-hour 11 kWh = 3.6 * 106J2. Suppose the cumulative energy used in a large building over a 24-hr period is givenby E(t) = 100t + 4t2 - t3/9kWh, where t = 0 corresponds tomidnight.a. Graph the energy function.b. The power is the rate of energy consumption; that is,P(t) = E′(t). Find the power over the interval 0≤ t ≤ 24.c. Graph the power function and interpret the graph. What are theunits of power in this case?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Power and energy Power and energy are often used interchangeably, but they are quite different. Energy is what makes matter
move or heat up. It is measured in units of joules or Calories,
where 1 Cal = 4184 J. One hour of walking consumes roughly106J, or 240 Cal. On the other hand, power is the rate at which
energy is used, which is measured in watts, where 1 W = 1 J/s.
Other useful units of power are kilowatts 11 kW = 103
W2 and megawatts 11 MW = 106 W2. If energy is used at a rate
of 1 kW for one hour, the total amount of energy used is
1 kilowatt-hour 11 kWh = 3.6 * 106
J2. Suppose the cumulative energy used in a large building over a 24-hr period is given
by E(t) = 100t + 4t2 - t3/9
kWh, where t = 0 corresponds to
midnight.
a. Graph the energy function.
b. The power is the rate of energy consumption; that is,
P(t) = E′(t). Find the power over the interval 0≤ t ≤ 24.
c. Graph the power function and interpret the graph. What are the
units of power in this case?
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