Power
Q. A 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds. What is the average power exerted by the engine?
A.
2000 W
B.
4000 W
C.
5000 W
D.
6000 W
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Solution
First, calculate the work done: W = (1/2)mv^2 = (1/2)(1000 kg)(20 m/s)^2 = 200000 J. Then, power is P = W/t = 200000 J / 10 s = 20000 W.
Correct Answer: C — 5000 W
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Q. A 1000 W heater operates for 1 hour. How much energy does it consume?
A.
3600 J
B.
1000 J
C.
3600000 J
D.
100000 J
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Solution
Energy consumed is E = P * t. Here, P = 1000 W and t = 1 hour = 3600 seconds. Thus, E = 1000 W * 3600 s = 3600000 J.
Correct Answer: C — 3600000 J
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Q. A 1000 W heater operates for 3 hours. How much energy does it consume?
A.
3000 J
B.
1080000 J
C.
3600000 J
D.
1000 J
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Solution
Energy consumed is E = P * t. Here, P = 1000 W and t = 3 hours = 10800 seconds. Thus, E = 1000 W * 10800 s = 10800000 J.
Correct Answer: C — 3600000 J
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Q. A 2000 W heater operates for 3 hours. How much energy does it consume in kilowatt-hours?
A.
6 kWh
B.
5 kWh
C.
4 kWh
D.
3 kWh
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Solution
Energy consumed in kilowatt-hours is calculated as E = P * t. Here, P = 2000 W = 2 kW and t = 3 hours. Thus, E = 2 kW * 3 h = 6 kWh.
Correct Answer: A — 6 kWh
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Q. A car engine does 3000 J of work in 5 seconds. What is the average power output of the engine?
A.
600 W
B.
800 W
C.
1000 W
D.
1200 W
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Solution
Using the formula P = W/t, we find P = 3000 J / 5 s = 600 W.
Correct Answer: C — 1000 W
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Q. A car engine does 3000 J of work in 5 seconds. What is the power of the engine?
A.
600 W
B.
800 W
C.
1000 W
D.
1200 W
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Solution
Using the formula P = W/t, we have P = 3000 J / 5 s = 600 W.
Correct Answer: A — 600 W
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Q. A cyclist exerts a force of 100 N to maintain a speed of 5 m/s. What is the power output of the cyclist?
A.
200 W
B.
500 W
C.
1000 W
D.
250 W
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Solution
Power can be calculated using P = F * v. Here, F = 100 N and v = 5 m/s. Thus, P = 100 N * 5 m/s = 500 W.
Correct Answer: B — 500 W
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Q. A cyclist is pedaling at a constant speed and exerts a power of 200 W. If the cyclist increases their power output to 400 W, what happens to their speed assuming no other forces act?
A.
Speed remains the same
B.
Speed doubles
C.
Speed increases by 41%
D.
Speed increases by 100%
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Solution
Power is proportional to the cube of the speed in cycling. If power doubles, speed increases by a factor of (2)^(1/3) which is approximately 1.26, or about a 41% increase.
Correct Answer: C — Speed increases by 41%
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Q. A light bulb uses 60 W of power. How much energy does it consume in 1 hour?
A.
3600 J
B.
216000 J
C.
60000 J
D.
180000 J
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Solution
Energy consumed can be calculated using E = P * t. Here, P = 60 W and t = 1 hour = 3600 seconds. Thus, E = 60 W * 3600 s = 216000 J.
Correct Answer: B — 216000 J
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Q. A light bulb uses 60 W of power. How much energy does it consume in 2 hours?
A.
120 J
B.
7200 J
C.
432000 J
D.
360 J
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Solution
Energy consumed can be calculated using E = P * t. Here, P = 60 W and t = 2 hours = 7200 seconds. Thus, E = 60 W * 7200 s = 432000 J.
Correct Answer: C — 432000 J
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Q. A light bulb uses 60 W of power. How much energy does it consume in 5 hours?
A.
18000 J
B.
108000 J
C.
300000 J
D.
360000 J
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Solution
Energy consumed can be calculated using E = P * t. Here, E = 60 W * (5 * 3600 s) = 108000 J.
Correct Answer: B — 108000 J
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Q. A light bulb uses 60 Watts of power. How much energy does it consume in 2 hours?
A.
120 Joules
B.
7200 Joules
C.
432000 Joules
D.
360000 Joules
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Solution
Energy consumed = Power × Time = 60 W × (2 × 3600 s) = 432000 J.
Correct Answer: C — 432000 Joules
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Q. A machine does 500 J of work in 10 seconds. What is its power output?
A.
50 W
B.
100 W
C.
200 W
D.
500 W
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Solution
Power is calculated using the formula P = W/t. Here, W = 500 J and t = 10 s, so P = 500 J / 10 s = 50 W.
Correct Answer: B — 100 W
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Q. A motor has a power rating of 1500 Watts. How much work can it do in 10 minutes?
A.
90000 Joules
B.
15000 Joules
C.
25000 Joules
D.
30000 Joules
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Solution
Work done = Power × Time = 1500 W × (10 × 60 s) = 90000 J.
Correct Answer: A — 90000 Joules
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Q. A person lifts a box of mass 10 kg to a height of 2 m in 4 seconds. What is the power exerted by the person?
A.
50 W
B.
25 W
C.
100 W
D.
75 W
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Solution
The work done against gravity is W = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J. Power is P = W/t = 196 J / 4 s = 49 W, approximately 50 W.
Correct Answer: A — 50 W
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Q. If 10^(2x) = 100, what is the value of x?
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Solution
100 = 10^2, so 2x = 2, hence x = 1.
Correct Answer: B — 0.5
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Q. If 10^x = 0.01, what is the value of x?
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Solution
Since 0.01 = 10^(-2), we have x = -2.
Correct Answer: A — -2
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Q. If 2^(x+1) = 16, what is the value of x?
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Solution
16 = 2^4 => x + 1 = 4 => x = 3
Correct Answer: B — 3
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Q. If 4^x = 64, what is the value of x?
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Solution
Since 64 = 4^3, we have x = 3.
Correct Answer: B — 3
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Q. If 5^(x+1) = 125, what is the value of x?
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Solution
125 = 5^3, so x + 1 = 3, hence x = 2.
Correct Answer: B — 2
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Q. If 5^x = 125, what is the value of x?
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Solution
125 = 5^3 => x = 3
Correct Answer: C — 3
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Q. If 5^x = 25, what is the value of x?
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Solution
Since 25 = 5^2, we have 5^x = 5^2, thus x = 2.
Correct Answer: B — 2
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Q. If 7^(x) = 49, what is the value of x?
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Solution
49 = 7^2, so x = 2.
Correct Answer: B — 2
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Q. If 8^(x) = 64, what is the value of x?
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Solution
64 = 8^2, so x = 2.
Correct Answer: B — 2
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Q. If a 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds, what is the average power output of the car's engine?
A.
2000 W
B.
4000 W
C.
6000 W
D.
8000 W
Show solution
Solution
First, calculate the work done: W = 0.5 * m * v^2 = 0.5 * 1000 kg * (20 m/s)^2 = 200000 J. Then, power is P = W/t = 200000 J / 10 s = 20000 W.
Correct Answer: C — 6000 W
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Q. If a 1000 W heater is used for 3 hours, how much energy does it consume in kilowatt-hours?
A.
3 kWh
B.
2 kWh
C.
1 kWh
D.
0.5 kWh
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Solution
Energy consumed in kilowatt-hours is calculated as E = P (kW) * t (h). Here, P = 1000 W = 1 kW and t = 3 hours. Thus, E = 1 kW * 3 h = 3 kWh.
Correct Answer: A — 3 kWh
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Q. If a car engine has a power output of 150 kW, how much work can it do in 2 minutes?
A.
18000 J
B.
9000 J
C.
30000 J
D.
180000 J
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Solution
Power is the rate of doing work. Work done can be calculated as W = P * t. Here, P = 150 kW = 150000 W and t = 2 minutes = 120 seconds. Thus, W = 150000 W * 120 s = 18000000 J.
Correct Answer: D — 180000 J
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Q. If a machine does 500 J of work in 10 seconds, what is its power output?
A.
50 W
B.
100 W
C.
200 W
D.
500 W
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Solution
Power is calculated using the formula P = W/t. Here, W = 500 J and t = 10 s. Thus, P = 500 J / 10 s = 50 W.
Correct Answer: B — 100 W
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Q. If a machine does 500 Joules of work in 10 seconds, what is its power output?
A.
50 Watts
B.
100 Watts
C.
200 Watts
D.
500 Watts
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Solution
Power is calculated as work done divided by time taken. Here, Power = 500 J / 10 s = 50 W.
Correct Answer: B — 100 Watts
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Q. If a machine has an efficiency of 80% and it consumes 1000 J of energy, what is the useful work output?
A.
800 J
B.
1000 J
C.
200 J
D.
600 J
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Solution
Useful work output can be calculated using the formula: Useful Work = Efficiency * Input Energy. Here, Useful Work = 0.8 * 1000 J = 800 J.
Correct Answer: A — 800 J
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