Understanding the distance a vehicle covers during a driver's reaction time is crucial in road safety calculations. This distance is known as the lag distance.

Understanding Lag Distance

Lag distance is the distance a vehicle travels from the moment the driver detects a situation requiring a stop or change in speed to the moment the brakes are actually applied. During this time, the vehicle continues to move at its initial speed because no deceleration has started yet. It depends only on the initial speed of the vehicle and the driver's reaction time.

The question provides us with the following information:

• Speed of the vehicle (V) = 100 kmph
• Reaction time of the driver (t) = 2.5 seconds
• Coefficient of friction (f) = 0.35 (Note: This value is relevant for calculating braking distance, but not for lag distance. The question specifically asks for lag distance during reaction time).

Calculating Lag Distance from Speed and Reaction Time

To calculate the lag distance, we need to use the formula:

Lag Distance = Speed $\times$ Reaction Time

First, the speed needs to be converted from kilometers per hour (kmph) to meters per second (m/s) to be consistent with the reaction time unit (seconds).

Conversion from kmph to m/s:

1 km = 1000 meters

1 hour = 3600 seconds

So, $100 \text{ kmph} = 100 \times \frac{1000 \text{ m}}{3600 \text{ s}}$

$100 \text{ kmph} = \frac{100000}{3600} \text{ m/s} = \frac{1000}{36} \text{ m/s} = \frac{250}{9} \text{ m/s}$

Step-by-Step Lag Distance Calculation

Now, we can calculate the lag distance using the converted speed and the given reaction time:

Speed (V) = $\frac{250}{9}$ m/s

Reaction time (t) = 2.5 s

Lag Distance = V $\times$ t

Lag Distance = $\frac{250}{9} \text{ m/s} \times 2.5 \text{ s}$

Lag Distance = $\frac{250}{9} \times \frac{5}{2} \text{ m}$

Lag Distance = $\frac{1250}{18} \text{ m}$

Lag Distance = $\frac{625}{9} \text{ m}$

Calculating the numerical value:

Lag Distance $\approx 69.44$ meters

Comparing with Options

The calculated lag distance is approximately 69.44 meters. Let's compare this with the given options:

• Option 1: 59.5 m
• Option 2: 49.5 m
• Option 3: 69.5 m
• Option 4: 79.5 m

The value 69.44 m is closest to 69.5 m.

Conclusion

The lag distance travelled by the vehicle during the driver's reaction time of 2.5 seconds, while travelling at a speed of 100 kmph, is approximately 69.5 meters.