The reaction time for an automobile driver is 0.7 sec. If the automobile can be decelerated at `5 "m/s"^2` calculate the total distance travelled in coming to stop from an initial velocity of 8.33 m/s after a signal is observed.

Options

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

Answer

To solve the problem, we need to calculate the total distance traveled by the automobile before it comes to a stop after the driver observes a signal. The process can be broken down into two main parts: the distance traveled during the driver's reaction time and the distance traveled while decelerating to a stop.

### Step 1: Calculate the distance traveled during the reaction time

The distance traveled during the reaction time can be calculated using the formula:

\[ S_r = u \times t \]

Where:
- \( S_r \) = distance during reaction time
- \( u \) = initial velocity (8.33 m/s)
- \( t \) = reaction time (0.7 s)

Substituting the values:

\[ S_r = 8.33 \, \text{m/s} \times 0.7 \, \text{s} \]

\[ S_r = 5.831 \, \text{m} \]

### Step 2: Calculate the distance traveled while decelerating

Next, we need to calculate the distance traveled while the car decelerates to a stop. We can use the third equation of motion:

\[ v^2 = u^2 + 2aS \]

Where:
- \( v \) = final velocity (0 m/s, since the car comes to a stop)
- \( u \) = initial velocity (8.33 m/s)
- \( a \) = acceleration (deceleration in this case, so it's -5 m/s²)
- \( S \) = distance traveled while decelerating

Rearranging the equation for \( S \):

\[ 0 = (8.33)^2 + 2(-5)S \]

This simplifies to:

\[ 0 = 69.3889 - 10S \]

Now, solving for \( S \):

\[ 10S = 69.3889 \]

\[ S = \frac{69.3889}{10} \]

\[ S = 6.93889 \, \text{m} \]

### Step 3: Calculate the total distance traveled

The total distance \( S_t \) is the sum of the distance during the reaction time and the distance while decelerating:

\[ S_t = S_r + S \]

Substituting the values we calculated:

\[ S_t = 5.831 \, \text{m} + 6.93889 \, \text{m} \]

\[ S_t = 12.76989 \, \text{m} \]

Rounding to two decimal places, we get:

\[ S_t \approx 12.77 \, \text{m} \]

### Final Answer

The total distance traveled by the automobile before coming to a stop is approximately **12.77 meters**.

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