To determine the time it takes for the vehicle to gain a velocity of 20 m/s with an acceleration of 2 m/s^2, we can use the equation of motion:
v = u + at
where: v is the final velocity (20 m/s), u is the initial velocity (0 m/s, as the vehicle starts from rest), a is the acceleration (2 m/s^2), and t is the time we want to find.
Rearranging the equation, we have:
t = (v - u) / a
Substituting the given values:
t = (20 m/s - 0 m/s) / 2 m/s^2
t = 20 m/s / 2 m/s^2
t = 10 s
Therefore, it will take 10 seconds for the vehicle to reach a velocity of 20 m/s with an acceleration of 2 m/s^2.