# To stop the car, the brakes must do work on the car. The driver applies brakes, which provide a constant braking force of 10kN. How far will the car travel before it stops?

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### 1 Answer

When the brakes are applied, the braking force causes a deceleration to stop the car. Using Newton's second law of motion, the applied braking force will cause a deceleration (negative acceleration) of car, that can be mathematically written as:

Braking force, F = mass (m) x acceleration (a) = mass (m) x deceleration (d)

We can also use other equation of motion relating the distance to velocity, acceleration and time as:

S = vt - 1/2 at^2

Since the final velocity of car is 0 (at rest),

S = -1/2 at^2 = -1/2 (-d)t^2 = 1/2dt^2 (where d is deceleration)

Here, we do not have the time it takes to decelerate. We can also use the other equation:

V^2 = u^2 + 2aS

or, 2aS = - u^2 = -2dS

S = u^2/2d = u^2 / 2(F/m) = mu^2 / 2F

= mu^2 / 20000

Here, we will need the mass of car and initial velocity.

Thus, to determine the stopping distance, we need some additional parameters, such as mass of car, initial velocity and/or time to stop.

For example, lets say the car weighs 1500 kg and its initial velocity is 90 km/hr (= 25 m/sec). Then the stopping distance is:

S = 1500 x 25 x 25/20000 = 46.87 m.

Thus, it will take about 47 m for the car to stop using the example case.

Hope this helps.