A constant force acted on a body of mass nine kilograms, such that its speed changed from 58 kilometres per hour to 66 kilometres per hour in one-half a second. Calculate the magnitude of the force.
In order to calculate the magnitude of the force, we will use Newton’s second law. This states that force is equal to mass multiplied by acceleration or 𝐹 equals 𝑚𝑎. We know that the mass of the body is equal to nine kilograms. However, currently, we don’t know the acceleration. Acceleration can be measured in metres per second squared or metres per second per second. This means that we can calculate it by dividing the change in velocity by the time.
In order to do this, the change in velocity must be measured in metres per second and the time in seconds. Our velocities or speeds are currently in kilometres per hour. We know that there are 1000 metres in one kilometre. 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. The change in velocity can be calculated in kilometres per hour by subtracting 58 from 66. This is equal to eight kilometres per hour. Multiplying this by 1000 gives us 8000. We can therefore say that the change in velocity is 8000 metres per hour.
Dividing 8000 by 3600 gives us 20 over nine or 20 ninths. The change in velocity is equal to 20 ninths metres per second. We can now calculate the acceleration by dividing 20 ninths by one-half. Dividing by one-half is the same as multiplying by two. This means that the acceleration is 40 ninths metres per second squared. We can now use this value to calculate the force. As the mass of the body was nine kilograms, the force is equal to nine multiplied by 40 ninths. The nines on the numerator and denominator cancel.
The magnitude of the force acting on the body is therefore 40 newtons.