A vehicle starts moving in a straight line with acceleration $a = 4$ m/s$^2$ and initial velocity zero. After accelerating for time $t_1$, the vehicle moves uniformly for time $t_2$, and finally decelerates for time $t_1$ coming to a stop. The total time is $10$ s and the average velocity is $5.1$ m/s. The time taken during acceleration $t_1$ is