The thinking distance is the distance travelled after you notice some danger and you apply the brakes. To get it we have to remember that the distance is given by:
![d=vt](https://img.qammunity.org/2023/formulas/physics/high-school/ul87ey70wpm37hhqdwgyqp7gz2pid3bo3k.png)
where v is the speed and t is the time. Before we can use this formula we need to convert the velocity from mph to mps, let's do this:
![40(mi)/(h)\cdot(1h)/(3600s)=(1)/(90)mps](https://img.qammunity.org/2023/formulas/mathematics/college/myyhishzmm34wo4h7vukh1jpc8gb2aytfp.png)
This means that we travel 1/90 mps; now that we have this we use the formula for the distance:
![d=((1)/(90))(2)=(1)/(45)=0.022](https://img.qammunity.org/2023/formulas/mathematics/college/myeyywiy6ale8thj8f3h0y74vu0hp0tutn.png)
Therefore, the thinking distance is 0.022 miles.