A constant force acted on a body of mass 𝑚 changing its speed from nine metres per second to 54 kilometres per hour. Given that the impulse of the force was 5.82 newton seconds, determine the value of 𝑚.
The first thing to note here is that our two speeds are in different units. We have nine metres per second and 54 kilometres per hour. There are 1000 metres in one kilometre. There are 3600 seconds in one hour. This means that to convert from kilometres per hour to metres per second, we can firstly multiply by 1000. We then divide this answer by 3600. 54 multiplied by 1000 is equal to 54000. So 54 kilometres per hour is equal to 54000 metres per hour. Dividing this by 3600 gives us 15. Therefore, 54 kilometres per hour is equal to 15 metres per second. We now have both of our speeds in the same units.
We’re told that the impulse of the force was 5.82 newton seconds. We know that impulse is equal to the mass multiplied by the change in velocity. The change in velocity can be measured in metres per second. The mass is measured in kilogrammes. Impulse can be measured in kilogramme metres per second. These are the same as newton seconds. Substituting in our values gives us 5.82 is equal to 𝑚 multiplied by six. We calculate the change in velocity by working out the difference between nine metres per second and 15 metres per second. 15 minus nine is equal to six. Dividing both sides of the equation by six gives us 𝑚 is equal to 5.82 divided by six. This is equal to 0.97.
Therefore, the mass of the body is 0.97 kilogrammes.