A driver of a 7550 N car passes a sign stating "Bridge Out 25 Meters Ahead." She slams on the brakes, coming to a stop in 10 s. How much work must be done by the brakes on the car if it is to stop just in time? Neglect the weight of the driver, and assume that the negative acceleration of the car caused by the braking is constant.

To calculate the work done by the brakes on the car, we need to find the force exerted by the brakes and the distance over which this force acts.

The force exerted by the brakes can be calculated using Newton's second law of motion: F = ma, where F is the force, m is the mass of the car, and a is the acceleration.

Given that the weight of the car is 7550 N, we can find the mass of the car using the formula: weight (W) = mass (m) x acceleration due to gravity (g).

Rearranging the formula gives us: m = W/g.

Substituting the given values: m = 7550 N / 9.8 m/s², we find m ≈ 771 kg.

Since the car comes to a stop in 10 s, the deceleration is given by the formula: a = (final velocity - initial velocity) / time.

Assuming the initial velocity is zero, the equation simplifies to: a = -final velocity / time.

Since the car stops just in time, the final velocity is also zero. Thus, a = -0 / 10 s = 0 m/s².

The force exerted by the brakes can now be calculated: F = ma = 771 kg x 0 m/s² = 0 N.

Since the force is now known to be zero, the work done by the brakes is also zero.

To find the amount of work done by the brakes on the car, we need to first calculate the deceleration of the car. We can then use this deceleration to calculate the net force acting on the car and finally calculate the work done.

Step 1: Calculate the deceleration of the car.
The deceleration can be calculated using the equation:

acceleration = (final velocity - initial velocity) / time

The final velocity is 0 m/s because the car comes to a stop, the initial velocity can be calculated using the equation:

initial velocity = √((2 * acceleration * distance))

where distance is the total distance traveled from the sign to the point where the car comes to a stop.

In this case, the distance is given as 25 meters.

Step 2: Calculate the net force on the car.
The net force acting on the car can be calculated using the equation:

force = mass * acceleration

The mass of the car is given as 7550 N. Remember to convert this to kg (divide by 9.8 m/s^2, acceleration due to gravity).

Step 3: Calculate the work done by the brakes.
The work done by the brakes is given by the equation:

work = force * distance

where force is the net force on the car and distance is the same 25 meters.

By following these steps, you can calculate the work done by the brakes on the car.