Overtaking time required for a vehicle with design speed 25 m/s and overtaking acceleration 1.0 m/sec² to overtake a vehicle moving at a speed 15 m/s, is:

Explanation:

To calculate the overtaking time required for a vehicle to overtake another vehicle, we can use the formula:

\(t = \frac{v_{\text{overtaken}} - v_{\text{overtaking}}}{a} \)

where:

\(v_{\text{overtaken}}\)​ is the speed of the overtaken vehicle.

\(v_{\text{overtaking}}\) is the speed of the vehicle being overtaking.

Given data:

\(v_{\text{overtaken}}\) = 15 m/s

\(v_{\text{overtaking}}\) = 25 m/s

a = 1.0 m/sec2

Calculation:

The relative speed difference between the overtaking vehicle and the overtaken vehicle is:

\(\Delta v = v_{\text{overtaking}} - v_{\text{overtaken}} \)

Δv= 25m/s−15m/s= 10m/s

Using the formula to calculate the overtaking time (t):

\(t = \frac{\Delta v}{a} \)

\(t = \frac{10 \, \text{m/s}}{1.0 \, \text{m/s}^2} \)

\(t = 10 \, \text{secs}\)