A car is approach a corner too fast and locks up the brakes at point A and holds them on for 12.5 M to point B. The car then moves from point B at a constant speed and does into the corner. At Point C because the car is still going to fast it goes out of control and leave the road the mass of the care is 850 kg. The radius of the corner is 20.0m. The force of friction between the tires and the road is 38250N in the corner as well as between points A and B. Calculate the minimum speed that the car must have had at point A.

To calculate the minimum speed that the car must have had at point A, we can use the concept of centripetal force.

First, let's analyze the different forces acting on the car at point C when it goes out of control and leaves the road. At point C, the only force acting on the car is the force of friction between the tires and the road, which is equal to 38250 N.

Now, let's calculate the maximum frictional force that the car can experience without slipping at point A. Since the car locks up its brakes at point A, the frictional force is at its maximum. This maximum frictional force is also equal to 38250 N.

The maximum frictional force between the tires and the road can be calculated using the formula:

Frictional Force = Mass * Acceleration

Where the acceleration is the centripetal acceleration. The centripetal acceleration can be calculated using the formula:

Centripetal Acceleration = (Velocity^2) / Radius

Now, we can equate the maximum frictional force to the centripetal force at point A. The centripetal force is given by:

Centripetal Force = Mass * Centripetal Acceleration

Since the car is moving at a constant speed from point B to the corner, the centripetal acceleration remains the same throughout the motion. Therefore, the centripetal force at point A is equal to the centripetal force in the corner.

Setting up the equation:

38250 N = 850 kg * ((Velocity^2) / 20.0 m)

Rearranging the equation:

Velocity^2 = (38250 N * 20.0 m) / 850 kg

Simplifying the equation:

Velocity^2 = 900

Taking the square root of both sides:

Velocity = √900

Velocity = 30 m/s

So, the minimum speed that the car must have had at point A is 30 m/s.