A driver leaves his car without applying the hand brakes on a road inclined at an angle of 25 degrees. The car starts to roll down the road with the driver chasing from behind after moving a distance of 20 m the speed of the car is 5.0 ms-1. Calculate the coefficient of static friction between the tyres and the road.

Someone please helppp. And explain please thanks!

To calculate the coefficient of static friction between the tires and the road, we can use the equation involving gravitational force and frictional force.

First, let's break down the forces acting on the car on the inclined road:

1. Gravitational Force (mg): This force acts vertically downward and is given by the formula:

F_gravity = m * g

where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. Normal Force (N): This force acts perpendicularly to the inclined road surface and is given by:

N = m * g * cos(θ)

where θ is the angle of inclination (25 degrees).

3. Frictional Force (f_friction): This force acts parallel to the inclined road surface and opposes the motion of the car. It is determined by the coefficient of static friction (μ_s) multiplied by the normal force:

f_friction = μ_s * N

Now, let's find the acceleration of the car. The net force acting on the car is equal to the force of gravity down the incline minus the frictional force:

Net force = F_gravity - f_friction

Since the car is accelerating down the incline, the net force is equal to the mass of the car times the acceleration:

m * a = F_gravity - f_friction

Plugging in the values we have:

m * a = m * g - μ_s * N

But we can substitute N using the equation for the normal force:

m * a = m * g - μ_s * (m * g * cos(θ))

Now we can solve for the acceleration (a):

a = g - μ_s * g * cos(θ)

Given that the car moves a distance of 20 m and its initial velocity is 5.0 m/s, we can use the following kinematic equation to find the time it takes for the car to travel that distance:

d = v_i * t + 0.5 * a * t^2

where:
d = distance (20 m)
v_i = initial velocity (5.0 m/s)
a = acceleration (calculated above)
t = time

Since the car starts from rest (v_i = 0), the equation simplifies to:

d = 0.5 * a * t^2

Solving for time (t):

t = sqrt((2 * d) / a)

Now, you can substitute the known values into the equation and calculate the time taken for the car to travel 20 m:

t = sqrt((2 * 20) / a)

With the time known, you can calculate the acceleration using the given distance and initial velocity values:

a = (vf^2 - v_i^2) / (2 * d)

Finally, substitute the value of acceleration back into the equation for friction:

a = g - μ_s * g * cos(θ)

Solve for μ_s:

μ_s = (g - a) / (g * cos(θ))