A reaction time for an automobile driver is 0.7 seconds. If the automobile can be decelerated at 0.5 m/s², calculate the total distance travelled in coming to stop from an initial velocity of 8.33 m/s after the signal is observed.

• A. 12.77 m
• B. 14.82 m
• C. 16.83 m
• D. 19.65 m

To find the total distance traveled by the automobile before it comes to a stop, we need to consider two phases: the reaction time and the braking distance.

Phase 1: Reaction Time

During the reaction time of 0.7 seconds, the car continues to move at its initial speed of 8.33 m/s. The distance covered during this time can be calculated using the formula:

• Distance = Speed × Time

Substituting the values:

• Distance = 8.33 m/s × 0.7 s = 5.831 m

Phase 2: Braking Distance

Next, we calculate the distance the car travels while decelerating. The formula for the stopping distance when deceleration is constant is:

• Distance = (Initial Velocity²) / (2 × Deceleration)

Using the values:

• Distance = (8.33 m/s)² / (2 × 0.5 m/s²) = 69.3889 m / 1 = 69.3889 m

Total Distance

Now, we add the distance covered during the reaction time and the braking distance:

• Total Distance = Reaction Distance + Braking Distance
• Total Distance = 5.831 m + 69.3889 m = 75.2199 m

However, this value seems incorrect based on the options provided. Let's re-evaluate the braking distance calculation:

Using the correct formula for stopping distance:

• Braking Distance = (Initial Velocity × Time) + (0.5 × Deceleration × Time²)

First, we need to find the time taken to stop after the reaction time:

• Final Velocity = Initial Velocity + (Deceleration × Time)
• 0 = 8.33 m/s - (0.5 m/s² × Time)
• Time = 8.33 m/s / 0.5 m/s² = 16.66 s

Now, we can calculate the braking distance:

• Braking Distance = (8.33 m/s × 16.66 s) + (0.5 × 0.5 m/s² × (16.66 s)²)
• Braking Distance = 138.88 m + 69.44 m = 208.32 m

Adding the reaction distance:

• Total Distance = 5.831 m + 208.32 m = 214.151 m

Since this value is also not matching the options, let's simplify:

Using the correct stopping distance formula:

• Braking Distance = (Initial Velocity²) / (2 × Deceleration) = (8.33 m/s)² / (2 × 0.5 m/s²) = 69.3889 m

Finally, the total distance is:

• Total Distance = 5.831 m + 69.3889 m = 75.2199 m

After reviewing the calculations, the correct answer is not among the options provided. Please verify the initial conditions or the options given.