Final answer:
The drag racer takes approximately 8.34 seconds to complete the race, with an acceleration phase and a constant velocity phase.
Step-by-step explanation:
To find the time it takes for the drag racer to complete the race, we need to consider two parts of the race: the acceleration phase and the constant velocity phase. In the acceleration phase, the drag racer accelerates at a rate of 24.3 m/s² for 3.2 s. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can find that the final velocity at the end of the acceleration phase is 24.3 m/s² * 3.2 s = 77.76 m/s.
In the constant velocity phase, the drag racer maintains this final velocity. To calculate the time taken in this phase, we can use the equation s = vt, where s is the distance and t is the time. Rearranging the equation to solve for t, we get t = s / v. Plugging in the values, we have t = 400 m / 77.76 m/s ≈ 5.14 s.
Therefore, the total time it takes for the drag racer to complete the race is approximately 3.2 s (acceleration phase) + 5.14 s (constant velocity phase) = 8.34 s.