Questions: Stopping distance REACTION Braking Hazard Braking begins According to brake.org.uk, the average reaction time for an alert, sober driver is approximately 0.67 seconds. The braking distance for a car traveling 30 miles per hour is 45 feet. This means that the car will travel 45 feet between when the driver presses the brake and when the car comes to a complete stop. Part 1: Determining the Reaction Distance A car is driving down a street at 30 mph when the driver spots a ball entering the street ahead of them. How far does the car travel before the driver presses the brake? Part 2: Total Stopping Distance Once the car has begun braking, it travels a further 45 feet. What is the car's total stopping distance from when the ball is seen to when the car finally comes to a complete stop?

Stopping distance

REACTION
Braking
Hazard
Braking
begins

According to brake.org.uk, the average reaction time for an alert, sober driver is approximately 0.67 seconds. The braking distance for a car traveling 30 miles per hour is 45 feet. This means that the car will travel 45 feet between when the driver presses the brake and when the car comes to a complete stop.

Part 1: Determining the Reaction Distance

A car is driving down a street at 30 mph when the driver spots a ball entering the street ahead of them. How far does the car travel before the driver presses the brake?

Part 2: Total Stopping Distance

Once the car has begun braking, it travels a further 45 feet. What is the car's total stopping distance from when the ball is seen to when the car finally comes to a complete stop?

Transcript text: Stopping distance REACTION Braking Mazard Braking begins According to brake.org.uk, the average reaction time for an alert, sober driver is approximately 0.67 seconds. The braking distance for a car traveling 30 miles per hour is 45 feet. This means that the car will travel 45 feet between when the driver presses the brake and when the car comes to a complete stop. Part 1: Determing the Reaction Distance A car is driving down a street at 30 mph when the driver spots a ball entering the street ahead of them. How far does the car travel before the driver presses the brake? Part 2: Total Stopping Distance Once the car has begun breaking, it travels a further 45 feet. What is the car's total stopping distance from when the ball is seen to when the car finally comes to a complete stop? $\square$

Solution

Solution Steps

Step 1: Determine the Reaction Distance

The reaction distance is the distance the car travels during the driver's reaction time. To calculate this, we need to convert the car's speed from miles per hour to feet per second and then multiply by the reaction time.

Convert 30 miles per hour to feet per second: \[ 30 \, \text{mph} = 30 \times \frac{5280 \, \text{feet}}{3600 \, \text{seconds}} = 44 \, \text{feet per second} \]
Calculate the reaction distance using the reaction time of 0.67 seconds: \[ \text{Reaction Distance} = 44 \, \text{feet/second} \times 0.67 \, \text{seconds} = 29.48 \, \text{feet} \]

Step 2: Calculate the Total Stopping Distance

The total stopping distance is the sum of the reaction distance and the braking distance.

The braking distance is given as 45 feet.
Add the reaction distance to the braking distance: \[ \text{Total Stopping Distance} = 29.48 \, \text{feet} + 45 \, \text{feet} = 74.48 \, \text{feet} \]