physics

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +13.0 m/s^2. At t(subscript 1), the rocket engine is shut down and the sled moves with a constant velocity v until t(subscript 2). The total distance traveled by the sled is 5.30 x 10^3, and the total time is 90.0 s. Find t(subscript 1), t(subscript 2), and v.

Please show your work. Thank you very much!

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  1. a=13m/s²
    v = 0 + a*t1....(1)
    t1+t2=90....(2)
    S=0*t1+(1/2)a*(t1)² + v*t2....(3)
    Express v and t2 in terms of t1 and solve for t1 using the third equation.

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  2. Find the velocity at the end of the acceleration.

    v=13t1
    distance1= 1/2 13 t1^2

    distance2= velocity*time= 1/2 13 t1(90-t1)

    t2 is 90 sec
    5.3E3=1/2 13 t1^2+ 1/2 13 t1(90-t1)

    do the algebra, solve for t1.

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