Can you help me solve this physics problem? (velocity, acceleration)?

Question

A sled powered by a rocket engine starts from rest on a frozen lake, accelerates at 13.0 m/s~2 (meters per second squared). At point A, the engine shuts down and sled moves with constant velocity V until point B. The sled travels a total distance of 5.30x10~3 m(5.30 times ten to the third meters) and the total time is 90.0 seconds. Find A, B, and V.

Please, if you can help solve this problem, tell me how you did it, so I can solve other problems like it. Thank you!

Answer 1

During the acceleration phase, the velocity is
v(t)=13*t
and
s(t)=.5*13*t^2
v(tA)=vA=13*tA
and A=.5*13*tA^2
During the constant speed case

and s(t)=A+vA*(t-tA)
at point B
B=5300=A+vA*(tB-tA)

we also know that tA+tB=90

Our equations are
tA+tB=90
v(tA)=vA=13*tA
A=.5*13*tA^2
5300=A+vA*(tB-tA)
so
5300=.5*13*tA^2+
13*tA*((90-tA)-tA)

solve for tA
5300=7.5*tA^2+13*tA*(90-2*tA)

5300=7.5*tA^2+1170*tA-26*tA^2

18.5*tA^2-1170*tA+5300=0
tA=4.91 seconds
so tB=85.1 seconds
A=181 meters
V=63.8 m/s

Check, since we know B=5300
B=5299 (close enough)

j

Answer 2

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