Answer:
-0.45
Step-by-step explanation:
To find the coefficient of friction, we can use the equation:
mu = F / N
where mu is the coefficient of friction, F is the force of friction, and N is the normal force.
The normal force is equal to the weight of the car, which can be calculated as follows:
N = m * g
where m is the mass of the car and g is the acceleration due to gravity (which is approximately 10 m/s^2).
The force of friction is equal to the braking force applied to the car. In this case, we know that the car stops after traveling 25 meters, so we can use the equation:
d = (v^2 - u^2) / (2 * a)
to find the acceleration of the car. Here, d is the distance traveled (25 meters), v is the final velocity (0 m/s), u is the initial velocity (15 m/s), and a is the acceleration. Solving for a, we get:
a = (v^2 - u^2) / (2 * d)
= (0 - 15^2) / (2 * 25)
= -225 / 50
= -4.5 m/s^2
The braking force applied to the car is equal to the mass of the car multiplied by the acceleration. So, we can calculate the force of friction as follows:
F = m * a
Substituting in the values we have calculated, we get:
mu = F / N
= (m * a) / (m * g)
= a / g
= (-4.5 m/s^2) / (10 m/s^2)
= -0.45
So, the coefficient of friction is approximately -0.45.
It's worth noting that this answer assumes that the car is able to stop in a distance of 25 meters. In reality, the braking distance may be longer or shorter depending on various factors such as the condition of the road and the tires, the load on the car, and the effectiveness of the brakes.