A car that weighs 15,000 N is initially moving at 60 km/hr when the brakes are applied. The car is brought to a stop in 30 m. Assuming the force applied by the brakes is constant, determine the magnitude of the braking force

60 km/hr = 60000m/3600s = 50/3 m/s

so,
v = 50/3 - at
t = 50/(3a)

s = 50/3 t - 1/2 at^2
= (50/3)(50/(3a)) - (1/2)(a)(50/(3a))^2 = 30
a = 125/27

F = ma = (15000/9.8)(125/27) = 7086 N

as always, check my math

To determine the magnitude of the braking force, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = m * a).

First, let's convert the initial velocity from km/hr to m/s:
60 km/hr = 60,000 m/3600 s = 16.67 m/s

Next, we need to find the acceleration. We can use the equation of motion, which relates the initial velocity (v₀), final velocity (v), acceleration (a), and distance (d):
v² = v₀² + 2ad

Given:
v₀ = 16.67 m/s
v = 0 m/s (since the car is brought to a stop)
d = 30 m

Plugging in the values, we get:
0 = (16.67)² + 2a(30)

Simplifying the equation, we have:
0 = 277.78 + 60a

Rearranging the equation to solve for acceleration (a):
60a = -277.78
a = -277.78 / 60
a = -4.63 m/s²

Since the car is decelerating, the acceleration is negative.

Now we can calculate the magnitude of the braking force using Newton's second law of motion:
F = m * a

Given:
m = 15,000 N (mass in newtons can be calculated using the formula: mass (kg) = weight (N) / gravitational acceleration (9.8 m/s²))

Converting the weight to mass:
m = 15,000 N / 9.8 m/s² = 1,530.6 kg

Now we can calculate the magnitude of the braking force:
F = 1,530.6 kg * (-4.63 m/s²)
F ≈ -7,076 N

Therefore, the magnitude of the braking force is approximately 7,076 N. Note that the negative sign indicates that the force is acting in the opposite direction of motion, which represents deceleration.