If a car is speeding down a road at 40 (mph), how long is the stopping distance compared to the stopping distance if the driver were going at the posted speed limit of 25 ?
Express your answer as a multiple of the stopping distance at 25
V1^2 / V2^2 = (40)^2 / (25)^2 = 2.56.
Therefore, the stopping distance at 40
mph is 2.56 times the stopping distance
at 25mph.
how far would the car travel after slamming on the breales if it was initially moving at 75 mph?
To determine the stopping distance, we need to consider the reaction time and the braking distance.
1. Reaction time: The average reaction time for a driver is around 1.5 seconds. During this time, the driver realizes they need to stop and start applying the brakes.
2. Braking distance: The braking distance refers to the distance the car travels while it is slowing down or coming to a stop. It depends on factors like the car's speed and the road conditions.
Let's calculate the stopping distance at 25 mph first:
1. Reaction distance: At 25 mph, the car would typically travel around 55 feet during the driver's reaction time. This can be calculated using the formula: Reaction distance = (Speed × Time) ÷ Conversion factor. In this case, the conversion factor is 1.47 ft/s (feet per second), since we want to convert mph to feet per second. So, the calculation would be: (25 × 1.5) ÷ 1.47 = 25.5 feet.
2. Braking distance: The braking distance can vary depending on various factors, such as the car's conditions and the road. Let's assume a typical braking distance of around 80 feet at 25 mph.
Therefore, the total stopping distance at 25 mph would be: Reaction distance (25.5 feet) + Braking distance (80 feet) = 105.5 feet.
Now, let's calculate the stopping distance at 40 mph:
1. Reaction distance: Using the same formula as before, the reaction distance would be: (40 × 1.5) ÷ 1.47 = 40.8 feet.
2. Braking distance: Again, assuming a typical braking distance of around 80 feet at 40 mph.
Therefore, the total stopping distance at 40 mph would be: Reaction distance (40.8 feet) + Braking distance (80 feet) = 120.8 feet.
To compare the stopping distance at 40 mph to the stopping distance at 25 mph, we can calculate the ratio:
Stopping distance at 40 mph ÷ Stopping distance at 25 mph = 120.8 feet ÷ 105.5 feet ≈ 1.143.
So, the stopping distance at 40 mph is approximately 1.143 times the stopping distance at 25 mph.
To determine the stopping distance, we need to consider two components: the perception distance and the braking distance.
The perception distance is the distance traveled by the car from the moment the driver perceives the need to stop until they actually start braking. This distance depends on the reaction time of the driver and external factors. Let's assume the perception distance is the same for both speeds we are comparing.
The braking distance is the distance traveled by the car from the moment the brakes are applied until the car comes to a complete stop. It depends on the initial speed of the car, the braking force applied, and the friction coefficient between the tires and the road surface.
The stopping distance is the sum of the perception distance and the braking distance.
Given that the initial speed of the car is 40 mph, we need to find the braking distance at this speed and compare it to the braking distance at the posted speed limit of 25 mph.
To calculate the braking distance, we can use the formula:
braking distance = (initial speed^2) / (2 * acceleration)
Assuming a constant rate of deceleration during braking, we can take the acceleration as a negative value. The coefficient of friction between the tires and the road determines the effectiveness of braking and can vary. However, for the purpose of this explanation, let's assume it is constant.
Now, let's calculate the braking distances for both speeds:
For 40 mph:
initial speed = 40 mph
acceleration = -1 (assuming consistent deceleration and friction coefficient)
braking distance at 40 mph = (40^2) / (2 * -1)
For 25 mph:
initial speed = 25 mph
acceleration = -1
braking distance at 25 mph = (25^2) / (2 * -1)
To find the ratio of the stopping distance at 40 mph compared to 25 mph, we need to divide the braking distance at 40 mph by the braking distance at 25 mph:
ratio = (braking distance at 40 mph) / (braking distance at 25 mph)
This ratio will give you the multiple of the stopping distance at 25 mph.