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Question Video: Finding the Work Done by the Resistance on a Road Mathematics

A car is moving on a straight road with a constant velocity of 12 km/h. Given that the force generated by the engine of the car is 36 kg-wt, find the work done by the resistance of the road in one minute.

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Video Transcript

A car is moving on a straight road with a constant velocity of 12 kilometers per hour. Given that the force generated by the engine of the car is 36 kilogram-weight, find the work done by the resistance of the road in one minute.

In order to answer this question, we need to find the work done by the resistance of the road. And we know to calculate work, we multiply force and distance. We are told that a car is moving on a straight road with a constant velocity of 12 kilometers per hour. As it is traveling at a constant velocity, we know that the acceleration is equal to zero. We are told that the force generated by the engine of the car is 36 kilogram-weight. Since the acceleration is zero, we know that the sum of the forces in the horizontal direction also equals zero. The sum of the forces gives us 36 minus 𝑅 equals zero. So the resistance force 𝑅 is also equal to 36 kilogram-weight.

In order to calculate the distance traveled by the car in one minute, we can use the equations of motion or SUVAT equations. As the acceleration is zero, both the initial and final velocities are 12 kilometers per hour. Before using our equations of motion, we need to convert these into the standard units of meters per second. We know that there are 1000 meters in one kilometer and 3600 seconds in one hour. This means that, to convert from kilometers per hour to meters per second, we multiply by 1000 and then divide by 3600. This is the same as dividing by 3.6. 12 divided by 3.6 is 10 over three or ten-thirds. Both the initial and final velocity of the car are ten-thirds meters per second.

We know that the acceleration is zero meters per second squared. And we are interested in a time of 60 seconds. To calculate the distance 𝑠, we can either use 𝑠 is equal to 𝑢𝑡 plus a half 𝑎𝑡 squared or 𝑠 is equal to 𝑢 plus 𝑣 divided by two multiplied by 𝑡. Using the first equation, we are left with 𝑠 is equal to 10 over three multiplied by 60. This is equal to 200. The car travels a distance of 200 meters in one minute.

We can now calculate the work done by the resistance by multiplying negative 36 by 200. The resistive force has a negative value as this is acting against the motion. The work done is therefore equal to negative 7200 kilogram-weight meters.

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