$2.1.29.$ 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?
a
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 $: $$ ma = \mu mg $$ $$ \boxed{\mu = \frac{a}{g} = 0.4} $$
$$\mu ≈ 0.4\text{; }l ≈ 50 \text{ m}$$