A constant force acted on a body of mass six kilograms. As a result, its speed changed from 37 kilometres per hour to 49 kilometres per hour. Calculate the magnitude of the impulse of this force on the body.
We can calculate the impulse of a force by multiplying the mass by the change in velocity. The units of mass need to be in kilograms. The change in velocity needs to be in metres per second. This means that the units for impulse are kilogram metres per seconds. Our velocities, or speeds, are given in kilometres per hour. Therefore, our first step is to convert these into metres per second.
There are 3600 seconds in one hour as there are 60 seconds in a minute and 60 minutes in one hour. 60 multiplied by 60 is 3600. There are 1000 metres in one kilometre. This means that to convert from kilometres per hour to metres per hour, we multiply by 1000. And to convert from metres per hour to metres per second, we divide by 3600.
The change in velocity is the difference between 37 and 49 kilometres per hour. 49 minus 37 is equal to 12. We can convert this into metres per second by multiplying by 1000 and then dividing by 3600. This is equal to10 thirds metres per second, or 3.3 recurring metres per second. The mass of our body is six kilograms. So, to calculate the impulse, we multiply six by 10 thirds. Six and three are divisible by three, so this simplifies to two multiplied by 10. The impulse of the force on the body is 20 kilogram metres per second.