If the speed of a car is increased by 35%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver's reaction time.
Braking distance increases with the square of the initial velocity, because it depends upon the car's initial klietic energy.
What is the square of 1.35?
oh right!! i forgot about square rooting 1.35.
thank you!
To determine the factor by which the minimum braking distance will be increased, we need to consider the relationship between speed and braking distance.
According to the laws of physics, the braking distance of a car is directly proportional to the square of its speed. Mathematically, this relationship can be expressed as:
braking distance ∝ speed^2
Now, let's define the initial speed of the car as V, the initial minimum braking distance as D, and the increased speed as V + 35% of V, or 1.35V.
According to the proportional relationship stated above, we have:
D ∝ V^2
To find the new braking distance, D', corresponding to the increased speed, we substitute the new speed value:
D' ∝ (1.35V)^2
Expanding and simplifying, we have:
D' ∝ 1.8225V^2
Now, to determine the factor by which the minimum braking distance is increased, we need to calculate the ratio of the new braking distance to the initial braking distance.
factor = D' / D = (1.8225V^2) / (V^2)
Simplifying, we have:
factor = 1.8225
Therefore, the minimum braking distance will be increased by a factor of approximately 1.8225 when the speed of the car is increased by 35%, assuming all else remains the same.
To determine the factor by which the minimum braking distance will be increased, we need to understand the relationship between the speed of the car and the minimum braking distance. This relationship is commonly expressed by the equation:
Braking distance ∝ (Speed)²
This equation states that the braking distance is directly proportional to the square of the car's speed.
Now, let's calculate the factor by which the minimum braking distance will increase.
1. Let's assume the initial speed of the car is "S" and the initial minimum braking distance is "D".
2. If the speed of the car is increased by 35%, the new speed will be:
New Speed = S + 0.35S = 1.35S
3. Based on the equation, the initial braking distance can be calculated as:
D ∝ S²
4. Similarly, the new braking distance can be calculated as:
New Braking Distance ∝ (1.35S)²
5. To determine the factor by which the minimum braking distance is increased, we can compare the new braking distance to the initial braking distance:
Factor of increase = (New Braking Distance) / (Initial Braking Distance)
6. Substituting the values, we have:
Factor of increase = [(1.35S)²] / (S²)
7. Simplifying the equation:
Factor of increase = (1.8225S²) / (S²)
8. The S² terms cancel out, leaving us with:
Factor of increase = 1.8225
Therefore, the factor by which the minimum braking distance will be increased when the speed of the car is increased by 35% is 1.8225.