A 920kg car is 65m from a concrete barrier, travelling at 125km/h, when the driver notices and slams on the breaks. The frictional force acting on the car is 8500 N. Is ther driver able to stop the car before hitting the barrier.

To determine if the driver is able to stop the car before hitting the barrier, we need to calculate whether the deceleration provided by the brakes is sufficient to bring the car to a complete stop in the given distance.

First, let's convert the speed from km/h to m/s, as the unit of acceleration is in m/s^2. We do this by dividing the speed by 3.6:

125 km/h ÷ 3.6 = 34.7 m/s

Next, we can calculate the deceleration (negative acceleration) using Newton's second law of motion. The net force acting on the car is the difference between the applied braking force and the frictional force:

Net force = Applied force - Frictional force

The applied force is given by the mass of the car multiplied by its acceleration:

Applied force = mass × acceleration

Solving for acceleration, we get:

Acceleration = Net force / mass

Acceleration = (Applied force - Frictional force) / mass

Plugging in the given values:

Acceleration = (0 - 8500 N) / 920 kg

Acceleration = -9.24 m/s² (negative sign indicates deceleration)

Now that we have the acceleration, we can determine the time it would take for the car to come to a complete stop. We can use the kinematic equation:

Final velocity = Initial velocity + (acceleration × time)

Since the final velocity is 0 (car comes to a stop), we can rewrite the equation as:

0 = 34.7 m/s + (-9.24 m/s² × time)

Solving for time:

34.7 m/s = 9.24 m/s² × time

time = 34.7 m/s / 9.24 m/s²

time = 3.75 seconds

Now, let's calculate the distance the car would travel during this time using the equation:

Distance = Initial velocity × time + (0.5 × acceleration × time²)

Distance = 34.7 m/s × 3.75 s + (0.5 × -9.24 m/s² × (3.75 s)²)

Distance = 130.875 m - 65.625 m

Distance = 65.25 m

The car would travel a distance of 65.25 meters during the time it takes to come to a complete stop. Since the car's initial distance from the barrier is 65 meters, it would not be able to stop in time. Therefore, the driver would not be able to stop the car before hitting the barrier.

To determine if the driver is able to stop the car before hitting the barrier, we can use the equations of motion.

First, let's convert the car's initial velocity from km/h to m/s:
125 km/h = 125 * (1000 m / 3600 s) = 34.72 m/s

Next, let's calculate the acceleration of the car using the equation:
F = m * a

Where:
F is the frictional force acting on the car, which is given as 8500 N.
m is the mass of the car, given as 920 kg.
a is the acceleration of the car.

Rearranging the equation, we get:
a = F / m

a = 8500 N / 920 kg ≈ 9.24 m/s²

Now, let's use the equations of motion:

1. Final velocity (v) is 0 because the car needs to come to a stop.
2. Initial velocity (u) is 34.72 m/s.
3. Acceleration (a) is -9.24 m/s² (negative because it acts in the opposite direction of motion).
4. Distance (s) is 65 m.

We can use the equation s = (v² - u²) / (2a) to calculate the stopping distance.

Substituting the values, we get:
65 = (0² - (34.72)²) / (2 * -9.24)

Simplifying:
65 = (0 - 1207.7) / (-18.48)
65 = 1207.7 / 18.48
65 = 65.37

Since the stopping distance required (65.37 m) is greater than the distance to the barrier (65 m), the driver is not able to stop the car before hitting the barrier.