Lesson Worksheet: Power Mathematics

Given that a car’s maximum speed is 270 km/h and its engine generates a force of 96 kg-wt, determine the power of its engine.

A car with an engine of 164 hp is moving at its maximum speed of 216 km/h. Calculate the magnitude of the force generated by its engine.

A tractor has an engine of 187 hp and it is pulling against a force of 374 kg-wt. Find its maximum speed.

A car of mass 5 tonnes 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.

Some workers are loading boxes in the back of a truck. Each box has a mass of 75 kg and the height of the truck is 1 m. Given that the average total power that the group can work at is 0.5 hp, calculate the number of boxes they can load into the truck in a minute. Take .

At a particular instance, a train of mass 147 tonnes was accelerating along a horizontal section of track at 68 cm/s² against a resistive force of 50 kg-wt for each metric ton 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 person of mass 66 kg walked up an inclined plane to a height of 450 metres in 5 minutes. Determine their average power throughout the walk.

A train of mass 170 tonnes is moving along a horizontal section of track at a constant speed of 60 km/h. Given that the engine’s power output is 410 hp, find the magnitude of the resistance, , to the train’s motion per metric ton of the train’s mass.

A vehicle of mass 3 tonnes 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 .