A vehicle drives on Dry asphalt road at 40mph and suddenly apply the brake. The break reaction time was 50 Milliseconds. Find the Stopping distance

To calculate the stopping distance, we need to account for both the reaction distance and the braking distance.

The formula for stopping distance \( d_s \) can be expressed as:

\[
d_s = d_r + d_b
\]

Where:
- \( d_r \) is the reaction distance,
- \( d_b \) is the braking distance.

### Step 1: Calculate Reaction Distance

The reaction distance is the distance the vehicle travels during the driver's reaction time, which is:

\[
d_r = v \times t_r
\]

Where:
- \( v \) is the vehicle's speed in feet per second (fps),
- \( t_r \) is the reaction time in seconds.

The speed is given as 40 mph. First, we need to convert 40 mph to fps:

\[
v = 40 \times \frac{5280}{3600} = 58.67 \, \text{fps}
\]

Now, with a reaction time of 50 milliseconds (or 0.05 seconds):

\[
d_r = 58.67 \times 0.05 = 2.93 \, \text{feet}
\]

### Step 2: Calculate Braking Distance

The braking distance is the distance required to stop the vehicle once the brakes are applied. The formula for braking distance \( d_b \) on dry asphalt is:

\[
d_b = \frac{v^2}{2g \mu}
\]

Where:
- \( v \) is the vehicle's speed (in fps),
- \( g \) is the acceleration due to gravity (32.2 ft/s\(^2\)),
- \( \mu \) is the coefficient of friction for dry asphalt (typically \( \mu = 0.7 \)).

Substituting the values:

\[
d_b = \frac{(58.67)^2}{2 \times 32.2 \times 0.7}
\]

Let me calculate that.

The braking distance \( d_b \) is approximately 76.36 feet.

### Step 3: Calculate Total Stopping Distance

Now, we can add the reaction distance \( d_r \) and the braking distance \( d_b \) to find the total stopping distance:

\[
d_s = d_r + d_b = 2.93 + 76.36 = 79.29 \, \text{feet}
\]

Thus, the total stopping distance is approximately **79.29 feet**.

Would you like more details, or do you have any questions?

Here are five related questions you might find interesting:
1. How does the stopping distance change with different road conditions (e.g., wet or icy roads)?
2. What effect does increasing the speed have on the stopping distance?
3. How does the vehicle's mass affect braking distance?
4. What is the role of reaction time in emergency braking situations?
5. How do anti-lock braking systems (ABS) impact stopping distance?

**Tip**: The braking distance increases with the square of the speed, so doubling your speed can quadruple your stopping distance.

A vehicle drives on Dry asphalt road at 40mph and suddenly applies the brake. The brake reaction time was 50 milliseconds. Find the Stopping distance.

Learn how to calculate the stopping distance for a vehicle traveling at 40mph on dry asphalt with a brake reaction time of 50 milliseconds. This problem explores key physics concepts such as reaction distance, braking distance, and stopping distance calculations. Suitable for Grades 10-12.

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