https://file.aiquickdraw.com/mathbot/file/1729691335528q1t2ibyc.jpg

Figuur 4 toont de situatie bij deze opgave. De sportwagen weegt 2 ton en heeft een snelheid
1v 100 km/u wanneer de chauffeur een obstakel op de weg ziet. Hij doet er 0,75 s over om te
reageren en op de rem te trappen, waardoor de sportwagen gaat slippen. Gegeven is de statische
wrijvingscoëfficiënt 0,35 s  en de kinetische wrijvingscoëfficiënt 0,25 k  . Bepaal de afstand die
de sportwagen aflegt tot hij tot stilstand komt.

To solve the problem of determining the distance the sports car travels before coming to a stop, we need to approach it step by step, using physics principles such as kinematics and friction.

### Known dataTo solve the problem of determining the distance the sports car travels before coming to a stop, we need to approach it step by step, using physics principles such as kinematics and friction.

### Known 
- Mass of the car: \( m = 2 \, \text{tons} = 2000 \, \text{kg} \)
- Initial speed: \( v_1 = 100 \, \text{km/h} = 27.78 \, \text{m/s} \)
- Reaction time: \( t_{\text{reaction}} = 0.75 \, \text{s} \)
- Static friction coefficient: \( \mu_s = 0.35 \)
- Kinetic friction coefficient: \( \mu_k = 0.25 \)
- Gravitational acceleration: \( g = 9.81 \, \text{m/s}^2 \)

### Step 1: Distance during reaction time
During the reaction time, the car continues at a constant speed since the brakes are not applied yet. The distance covered in this time is:

\[
d_{\text{reaction}} = v_1 \times t_{\text{reaction}} = 27.78 \, \text{m/s} \times 0.75 \, \text{s} = 20.84 \, \text{m}
\]

### Step 2: Deceleration due to kinetic friction
Once the driver reacts and starts braking, the car begins to decelerate. The force of kinetic friction acting on the car is:

\[
F_{\text{friction}} = \mu_k \times m \times g = 0.25 \times 2000 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 4905 \, \text{N}
\]

The acceleration (which is negative due to deceleration) caused by this frictional force is:

\[
a = \frac{F_{\text{friction}}}{m} = \frac{4905}{2000} = 2.4525 \, \text{m/s}^2
\]

### Step 3: Distance during braking
The car decelerates from the initial speed \( v_1 = 27.78 \, \text{m/s} \) to 0 m/s. Using the kinematic equation:

\[
v^2 = u^2 + 2 a d
\]

where:
- \( v = 0 \, \text{m/s} \) (final velocity),
- \( u = 27.78 \, \text{m/s} \) (initial velocity),
- \( a = -2.4525 \, \text{m/s}^2 \) (negative due to deceleration),
- \( d \) is the stopping distance.

Solving for \( d \):

\[
0 = (27.78)^2 + 2 (-2.4525) d
\]

\[
d = \frac{(27.78)^2}{2 \times 2.4525} = \frac{771.81}{4.905} \approx 157.31 \, \text{m}
\]

### Step 4: Total distance
The total distance the car travels before stopping is the sum of the distance covered during the reaction time and the braking distance:

\[
d_{\text{total}} = d_{\text{reaction}} + d_{\text{braking}} = 20.84 \, \text{m} + 157.31 \, \text{m} = 178.15 \, \text{m}
\]

Thus, the total distance the car travels before coming to a stop is approximately **178.15 meters**.

Let me know if you would like more details on any step!

### Follow-up Questions:
1. How would the total distance change if the friction coefficient were higher?
2. What effect would a faster reaction time have on the overall stopping distance?
3. Can we compute the stopping distance if the car were traveling at a lower speed, say 60 km/h?
4. How would the stopping distance be affected if the car was heavier, say 3 tons?
5. What role does the difference between static and kinetic friction coefficients play in the stopping process?

### Tip:
When calculating stopping distances, always account for both the driver's reaction time and the braking distance, as both significantly contribute to the total stopping distance.

Figuur 4 toont de situatie bij deze opgave. De sportwagen weegt 2 ton en heeft een snelheid 100 km/u wanneer de chauffeur een obstakel op de weg ziet. Hij doet er 0,75 s over om te reageren en op de rem te trappen, waardoor de sportwagen gaat slippen. Gegeven is de statische wrijvingscoëfficiënt 0,35 en de kinetische wrijvingscoëfficiënt 0,25. Bepaal de afstand die de sportwagen aflegt tot hij tot stilstand komt.

In this physics problem, determine the stopping distance of a sports car moving at 100 km/h with a weight of 2 tons, given friction coefficients of 0.35 (static) and 0.25 (kinetic). Learn how to calculate the total stopping distance using kinematics and friction concepts.

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