Question

A car has a mass of 1070 kg and is moving in a straight line at a speed of 91.3 km/h what is the magnitude of the constant net force in N require to bring the car to rest over a distance of 128m?

Answer 1

We are asked to determine the force required to stop a car that is moving at a velocity of 91.3 km/h.

First, we will convert the 91.3 km/h into m/s. To do that we will use the following conversion factors:

`\begin{gathered} 1km=1000m \\ 1h=3600s \end{gathered}`

Multiplying the conversion factors we get:

`91.3(km)/(h)*(1000m)/(1km)*(1h)/(3600s)=25.36(m)/(s)`

Now. We use a balance of energy. The work done by the force to stop the car must be equal to the change in kinetic energy of the car, therefore, we have:

`W=(1)/(2)mv_f^2-(1)/(2)mv_0^2`

Since the car will stop this means that the final velocity is 0:

`W=-(1)/(2)mv_0^2`

The work done is equal to the product of the force and the distance:

`Fd=-(1)/(2)mv_0^2`

Now, we divide both sides by the distance "d":

`F=-(mv_0^2)/(2d)`

Substituting the values:

`F=-((1070kg)(25.36(m)/(s)))/(2(128m))`

Solving the operations:

`F=-106N`

Therefore, the magnitude of the force required is 106 Newtons.