How do you calculate the braking distance?
driver reaction time=0.6s
initial speed of car=30ms-1
Please show all the steps and the equations you used in words
the question states initial speed*2 is equal to = distance*4
If you need thinking distance it is stated to be 18m
car travels some distance before the brakes are applied; speed*time=.6*30 m
so it goes 18 m before the brakes are applied.
then, during braking, the car slows, it travels distance for stopping. your equation speed*2= distance*4 makes no sense to me.
To calculate the braking distance, we need to consider the thinking distance and the braking distance separately.
The thinking distance is the distance traveled by the car during the driver's reaction time, which is given as 0.6 seconds.
First, let's calculate the thinking distance. We are given the initial speed of the car as 30 m/s. We can use the formula:
thinking distance = initial speed * driver reaction time
Substituting the given values:
thinking distance = 30 m/s * 0.6 s
thinking distance = 18 meters
Next, let's calculate the braking distance. It is given that the initial speed multiplied by 2 is equal to the distance multiplied by 4. Therefore, we have the equation:
2 * initial speed = 4 * braking distance
Substituting the given value of the initial speed:
2 * 30 m/s = 4 * braking distance
Simplifying the equation:
60 m/s = 4 * braking distance
To isolate the braking distance, we divide both sides of the equation by 4:
60 m/s / 4 = braking distance
15 m/s = braking distance
So, the braking distance is 15 meters.
Therefore, the total stopping distance is the sum of the thinking distance and the braking distance:
total stopping distance = thinking distance + braking distance
total stopping distance = 18 meters + 15 meters
total stopping distance = 33 meters
To calculate the braking distance, you need to consider both the thinking distance and the braking distance itself.
Step 1: Calculate the thinking distance.
The thinking distance is the distance the car travels during the driver's reaction time. In this case, the driver reaction time is given as 0.6 seconds.
The formula to calculate the thinking distance is:
Thinking distance = Speed × Reaction time
Since the initial speed of the car is given as 30 m/s and the reaction time is 0.6 seconds:
Thinking distance = 30 m/s × 0.6 seconds = 18 meters
Therefore, the thinking distance is 18 meters.
Step 2: Calculate the braking distance.
The question states that the initial speed multiplied by 2 is equal to the total distance (thinking distance + braking distance) multiplied by 4. Since we have already calculated the thinking distance, we can use this information to find the braking distance.
Let's denote the braking distance as 'd'.
According to the question, we have the equation:
2 × initial speed = (thinking distance + braking distance) × 4
Substituting the values:
2 × 30 m/s = (18 m + d) × 4
Simplifying the equation:
60 m/s = (18 m + d) × 4
(18 m + d) = 60 m/s ÷ 4
(18 m + d) = 15 m/s
Now, isolate the braking distance:
d = 15 m/s - 18 m
d = -3 m
Since the calculated braking distance is negative, it indicates that the car would not be able to stop within the given reaction time and initial speed. In this case, the car would have collided with an obstacle or gone past the stopping point.
To calculate the braking distance correctly, the values used in the equation should be reviewed for accuracy.