Яку відстань проїде автомобіль до повної зупинки, якщо шофер різко гальмує при швидкості 72 км/год, а від початку гальмування до зупинки проходить 6 с?

1. Break Down the Problem

1.1. Convert the speed from km/h to m/s.
1.2. Use the formula for distance traveled during deceleration.
1.3. Calculate the distance using the initial speed, time, and the concept of uniform acceleration.

2. Relevant Concepts

• Conversion of speed:
  $v = \frac{72 \text{ km/h} \times 1000 \text{ m/km}}{3600 \text{ s/h}} = 20 \text{ m/s}$
• Distance formula for uniformly accelerated motion:
  $s = v_0 \cdot t + \frac{1}{2} a \cdot t^2$
• The acceleration $a$ can be calculated as follows:
  $a = \frac{v - v_0}{t} \quad \text{where } v = 0$

3. Analysis and Detail

3.1. First, calculate the acceleration:
$a = \frac{0 - 20 \text{ m/s}}{6 \text{ s}} = -\frac{20}{6} \approx -3.33 \text{ m/s}^2$

3.2. Now, using the distance formula:
$s = v_0 \cdot t + \frac{1}{2} a \cdot t^2$ Substituting values:
$s = 20 \text{ m/s} \cdot 6 \text{ s} + \frac{1}{2} \cdot (-3.33 \text{ m/s}^2) \cdot (6 \text{ s})^2$ $s = 120 \text{ m} + \frac{1}{2} \cdot (-3.33) \cdot 36$ $s = 120 \text{ m} - 59.88 \text{ m} \approx 60.12 \text{ m}$

4. Verify and Summarize

The distance traveled during the braking period is approximately $60.12$ m.

Final Answer

The car will travel approximately 60.12 meters before coming to a stop.