To solve this problem, we'll first convert the initial and final speeds from km/h to m/s, and then use the equations of motion to find the time required.
Given: Initial speed (u) = 30 km/h Final speed (v) = 90 km/h Acceleration (a) = 1.8 m/s^2
Converting the speeds to m/s: Initial speed (u) = 30 km/h * (1000 m/1 km) * (1 h/3600 s) = 8.33 m/s Final speed (v) = 90 km/h * (1000 m/1 km) * (1 h/3600 s) = 25 m/s
Using the equation of motion: v = u + at
Substituting the values: 25 m/s = 8.33 m/s + (1.8 m/s^2) * t
Simplifying: 25 m/s - 8.33 m/s = 1.8 m/s^2 * t 16.67 m/s = 1.8 m/s^2 * t
Now, solving for time (t): t = 16.67 m/s / 1.8 m/s^2 t ≈ 9.26 seconds
Therefore, it will take approximately 9.26 seconds for the vehicle to attain a speed of 90 km/h.