How long would it take a 3.4 kg bike with 79 kg rider traveling at 18.6 m/s to stop if 867 n of force is applied to the brakes?

1.76 s

Explanation:

We have the following data:

is the total mass of the bike and the rider

is the initial velocity

is the force applied to the brakes

Firstly, we will find the acceleration with the following equation:

(1)

Isolating :

(2)

(3)

(4) This is the magnitude of the acceleration, however, since the final velocity is 0 m/s, this means the direction is negative

Hence:

(5)

On the other hand, with the following equation we can find the time :

(6)

Where:

is the final velocity (the bike stops)

Isolating :

(7)

(8)

Finally:

This iste time it takes to the bike to stop