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Lesson Worksheet: Power Mathematics
In this worksheet, we will practice finding the power of a constant force using the relation 𝑃 = 𝐹 × 𝑣.
A car of mass 5 metric tons is moving along a straight horizontal road. The resistance to its motion is directly proportional to its speed. When the car is traveling at 78 km/h, the resistance is equal to 40 kg-wt per metric ton of the car’s mass. Given that the maximum force of the engine is 300 kg-wt, determine the car’s maximum speed and the power at which its engine operates at this speed.
A small aeroplane is flying horizontally. The air resistance is proportional to the square of its speed and was 520 kg-wt when it was moving at 205 km/h. Given that the maximum speed of the aeroplane is 300 km/h, determine the power of its engine, stating your answer to the nearest horsepower if required. Take .
At a particular instance, a train of mass 147 metric tons was accelerating along a horizontal section of track at 68 cm/s2 against a resistive force of 50 kg-wt for each tonne of its mass. Given that the maximum speed of the train along this section of track was 72 km/h, find the power of its engine.
A vehicle of mass 3 metric tons was moving at 51 km/h along a horizontal section of road. When it reached the bottom of a hill inclined to the horizontal at an angle whose sine is 0.5, it continued moving at the same speed up the road. Given that the resistance of the two sections of road is constant, determine the increase in the vehicle’s power to the nearest horsepower. Take the acceleration due to gravity .