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An ice shed powered by a rocket engine starts from rest on a large frozen lake and accelerates at 40 ft/s2. After some time t1, the rocket engine is shut down adn the sled moves with constant velocity v for a time t2. If the total distance traveled by the sled is 17500 ft and the total time is 90 s, find t1 and t2

My work so far... I divided the work into two parts: shed that accelerated and the shed that moves in constant motion. Since I know the equation is d = vi + 0.5at2. I plugged in 0 for vi, since the rocket starts from rest. I plugged in a for 40 ft/s2. Since I don't know what t and d are, I just left them there. I got d1 = 20ti2 Next, since I know d1 + d2 = 17500 ft and t1 + t2 is 90s, I plugged 20ti2 into d1 and got 20ti2 + t2 = 90s. What should I do next??? I tried 3 hours on this hk problem, using different equations. But since I don't know the final velocity, I can't use any other equations for acceleration. I tried to use the value of the total distance, 17500 and total time 90s on equation d = 0.5 (vi + vf)t, but the velocity isn't constant so I can't do anything about it.

My work so far... I divided the work into two parts: shed that accelerated and the shed that moves in constant motion. Since I know the equation is d = vi + 0.5at2. I plugged in 0 for vi, since the rocket starts from rest. I plugged in a for 40 ft/s2. Since I don't know what t and d are, I just left them there. I got d1 = 20ti2 Next, since I know d1 + d2 = 17500 ft and t1 + t2 is 90s, I plugged 20ti2 into d1 and got 20ti2 + t2 = 90s. What should I do next??? I tried 3 hours on this hk problem, using different equations. But since I don't know the final velocity, I can't use any other equations for acceleration. I tried to use the value of the total distance, 17500 and total time 90s on equation d = 0.5 (vi + vf)t, but the velocity isn't constant so I can't do anything about it.

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