An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at 14.3 m/s².

At [tex]t_1[/tex] seconds, the rocket engine is shut down, and the sled moves with constant velocity [tex]v[/tex] for another [tex]t_2[/tex] seconds. The total distance traveled by the sled is [tex]5.56 \times 10^3[/tex] meters, and the total time is 98.3 seconds.

1. Find [tex]t_1[/tex].
- Answer in units of seconds.

2. Find [tex]t_2[/tex].
- Answer in units of seconds.

In this physics problem, the rocket sled accelerates for about 28 seconds (t1), and then moves at a constant velocity for about 70.3 seconds (t2).

Explanation:

Calculation of t1 and t2 for an ice sled powered by a rocket

The problem involves two parts: the time while the rocket is accelerating (t1), and the time it moves at constant velocity (t2). We are given the total distance the sled traveled (5.56 x 10^3 m) and the total time of travel (98.3 sec).

The sled travels at a constant acceleration (14.3 m/s²) for t1 seconds, so using the equation for distance under constant acceleration, d = 0.5*a*t1², and substituting, 0.5 * 14.3 m/s² * t1² = 5.56 x 10^3 m. Solving this for t1, we get approximately 28 seconds.

Then, the total time is t1 + t2, so 98.3 s = 28 s + t2. Solving for t2, we get t2 is approximately 70.3 seconds.

The time t1 where the sled accelerates is around 28 seconds, the time t2 where the sled moves with constant speed is around 70.3 seconds.

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