A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#2.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $2.1.29.$ A car with a powerful engine, starting from a place, gains a speed of $72$ $\frac{km}{h}$ in $5$ seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?
    </p>

    <h3>Solution</h3>
    <p>
        a<center>

Finding the deceleration value $$a = -\frac{\Delta v}{\Delta t} = -4 \\,\frac{m}{s}$$

$$\Delta t = \frac{\Delta v}{a}$$
2. The kinematic equations of motion in this case are represented as follows:
$$\boxed{x=v_0t-\frac{v \Delta t^2}{2}=\frac{v_0^2}{2a}=50 \,m}$$
Let's find the coefficient of friction $\mu$:
$$ma = \mu mg$$

$$\boxed{\mu = \frac{a}{g} = 0.4}$$

    <h4>Answer</h4>
    <p>
        $$\mu  ≈ 0.4\text{; }l ≈ 50 \text{ m}$$
    </p>


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