The typical reaction time for most drivers is considered to be about 1.50s. Traffic safety engineers often use a deceleration value of 5.85m/s2to calculate the minimum stopping distance for a vehicle on smooth, dry pavement. Determine the distance travelled while reacting, the distance travelled while braking, and the minimum stopping distance of a vehicle travelling 110km/h.
To determine the distance traveled while reacting, we need to use the given reaction time and the initial velocity of the vehicle. Here's how to calculate it step by step:
Step 1: Convert the given reaction time to seconds.
Given reaction time = 1.50s
Step 2: Convert the initial velocity from km/h to m/s.
Given initial velocity = 110 km/h
Convert km/h to m/s: 110 km/h × (1000 m/3600 s) = 30.56 m/s
Step 3: Calculate the distance traveled while reacting using the formula:
Distance traveled while reacting = Reaction time × Initial velocity
Distance traveled while reacting = 1.50 s × 30.56 m/s
Now, let's calculate the result:
Distance traveled while reacting = 45.84 m (rounded to two decimal places)
To determine the distance traveled while braking, we need to use the deceleration value provided. Here's how to calculate it step by step:
Step 1: Calculate the deceleration from the given value.
Given deceleration = 5.85 m/s^2
Step 2: Calculate the time taken to stop the vehicle using the deceleration.
Time taken to stop = Initial velocity / Deceleration
Time taken to stop = 30.56 m/s / 5.85 m/s^2
Now, let's calculate the result:
Time taken to stop = 5.23 s (rounded to two decimal places)
Step 3: Calculate the distance traveled while braking using the formula:
Distance traveled while braking = (Initial velocity × Time taken to stop) - (0.5 × Deceleration × Time taken to stop^2)
Distance traveled while braking = (30.56 m/s × 5.23 s) - (0.5 × 5.85 m/s^2 × (5.23 s)^2)
Now, let's calculate the result:
Distance traveled while braking = 80.14 m (rounded to two decimal places)
To determine the minimum stopping distance, we need to sum the distance traveled while reacting and the distance traveled while braking. Here's how to calculate it:
Minimum stopping distance = Distance traveled while reacting + Distance traveled while braking
Minimum stopping distance = 45.84 m + 80.14 m
Now, let's calculate the result:
Minimum stopping distance = 125.98 m (rounded to two decimal places)
Therefore, the distance traveled while reacting is 45.84 meters, the distance traveled while braking is 80.14 meters, and the minimum stopping distance of the vehicle traveling at 110 km/h is 125.98 meters.