We can use the kinematic equation that relates the final velocity (v), initial velocity (u), acceleration (a), and time (t):
v = u + at
Here, u = 0 (since the vehicle starts from rest), a = 2 m/s^2, and v = 20 m/s. Substituting these values into the equation, we get:
20 m/s = 0 + 2 m/s^2 × t
Simplifying and solving for t, we get:
t = 20 m/s ÷ (2 m/s^2)
t = 10 seconds
Therefore, it will take 10 seconds for the vehicle to gain the velocity of 20 m/s, assuming the acceleration remains constant.