A 1500 kg automobile travels at a speed of 105 km/h along a straight concrete highway. Faced with an emergency situation, the driver jams on the brakes, and the car skids to a stop.

(a) What will be the car's stopping distance for dry pavement (µ = 0.85)?
(b) What will be the car's stopping distance for wet pavement (µ = 0.60)?

so for this problem, do you use kinematic equations?

Jnb

Yes, we can use kinematic equations to solve this problem. Specifically, we will be using the equation of motion that relates distance, initial velocity, final velocity, acceleration, and time:

\[d = \frac{1}{2}(v_i + v_f)t\]

In this case, we know the initial velocity (105 km/h), which we need to convert to meters per second (m/s) since the standard unit of acceleration is m/s^2. Additionally, we need to calculate the time it takes for the car to come to a stop (t), and the final velocity (v_f) will be 0 m/s. Finally, we need to calculate the acceleration (a), which can be obtained from the equation:

\[a = \mu \cdot g\]

where μ is the coefficient of friction for the given surface and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Using these equations, we can solve for the stopping distance for dry and wet pavements. Let's calculate them step by step.

(a) Stopping distance for dry pavement (μ = 0.85):
Given:
Mass of the car (m) = 1500 kg
Initial velocity (v_i) = 105 km/h

1. Convert the initial velocity from km/h to m/s:
\[v_i = \frac{105 \, \text{km/h}}{3.6} = 29.17\, \text{m/s}\]

2. Calculate the final velocity (v_f) = 0 m/s.

3. Calculate the acceleration (a) using the coefficient of friction (μ = 0.85):
\[a = 0.85 \cdot 9.8 \, \text{m/s}^2\]

4. Calculate the time taken (t) to come to a stop:
Using the equation: \(v_f = v_i + at\) and rearranging the equation to solve for t, we get:
\[t = \frac{v_f - v_i}{a}\]

Plugging in the values: \(t = \frac{0 - 29.17}{a}\)

5. Calculate the stopping distance (d) using \(d = \frac{1}{2}(v_i + v_f)t\).

(b) Stopping distance for wet pavement (μ = 0.60):
Repeat steps 1 to 5 using the new coefficient of friction (μ = 0.60) to calculate the stopping distance for wet pavement.

I hope this explanation helps you solve the problem step by step!